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The Work of Yoshihiro Shibata

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Recent Developments of Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

Introducing his research carrier, we address Prof. Yoshihiro Shibata’s great contributions to the mathematical analysis. His out-standing influence to the mathematical society is also clarified.

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List of Publications of Yoshihiro Shibata

  1. T. Abe, Y. Shibata, On the Stokes and Navier-Stokes flows between parallel planes, in Harmonic Analysis and Nonlinear Partial Differential Equations (Japanese) (1235) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 2001), pp. 160–191

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  3. T. Abe, Y. Shibata, On a generalized resolvent estimate of the Stokes equation on an infinite layer, Part 1 \(\vert \lambda \vert> 0\) case. J. Math. Soc. Jpn. 55(2), 469–497 (2003)

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  4. T. Akiyama, H. Kasai, Y. Shibata, M. Tsutsumi, On a resolvent estimate of a system of Laplace operators with perfect wall condition. Funkcial. Ekvaj. 47(3), 361–394 (2004)

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  5. T. Akiyama, Y. Shibata, On an L p approach to the stationary and non-stationary problems to the Ginzburg-Landau-Maxwell equations. J. Differ. Equ. 243(1), 1–23 (2007)

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  6. P. D’Ancona, Y. Shibata, On global solvability of nonlinear viscoelastic equations in the analytic category. Math. Meth. Appl. Sci. 17(6), 477–486 (1994)

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  7. W. Dan, Y. Shibata, On the L q –L r estimate of the Stokes semigroup in a two dimensional exterior domain. J. Math. Soc. Jpn. 51(1), 181–207 (1999)

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  8. W. Dan, T. Kobayashi, Y. Shibata, On the local energy decay approach to some fluid flow in an exterior domain, in Recent Topics on Mathematical Theory of Viscous Incompressible Fluid (Tsukuba, 1996), Lecture Notes Numerical Application Analysis, vol. 16 (Kinokuniya, Tokyo, 1998), pp. 1–51

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  9. W. Dan, Y Shibata, On a local energy decay of solutions of a dissipative wave equation. Funkcial. Ekvaj. 38(3), 545–568 (1995)

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  10. W. Dan, Y. Shibata, On the L p -L q estimates of the Stokes semigroup in a two-dimensional exterior domain, in Nonlinear Evolution Equations and Their Applications (Japanese) (Kyoto, 1996) (1009) (Sūrikaisekikenkyūsho Kōkyūroku, 1997), pp. 79–99

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  11. W. Dan, Y. Shibata, Remark on the L q –\(L_{\infty }\) estimate of the Stokes semigroup in a two dimensional exterior domain. Pacific J. Math. 189(2), 223–239 (1999)

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  12. R. Denk, R. Racke, Y. Shibata, L p theory for the linear thermoelastic plate equations in bounded and exterior domains. Adv. Differ. Equ. 14(7–8), 685–715 (2009)

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  13. R. Denk, R. Racke, Y. Shibata, Local energy decay estimate of solutions to the thermoelastic plate equations in two- and three- dimensional exterior domains. Z. Anal. Anwend. 29(1), 21–62 (2010)

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  14. Y. Enomoto, Y. Shibata, Local energy decay of solutions to the Oseen equation in the exterior domains. Indiana Univ. Math. J. 53(5), 1291–1330 (2004)

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  15. Y. Enomoto, Y. Shibata, On the rate of decay of the Oseen semigroup in exterior domains and its application to Navier-Stokes equations. J. Math. Fluid Mech. 7(3), 339–367 (2005)

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  16. Y. Enomoto, Y. Shibata, On a Stability theorem of the navier-stokes equation in an exterior domain. in Hyperbolic Problems, Theory, Numerics and Applications I (Yokohama Publisher, Yokohama, 2006), pp. 383–389

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  17. Y. Enomoto, Y. Shibata, On some decay properties of Stokes semigroup of compressible viscous fluid flow in a 2-dimensional exterior domain. J. Differ. Equ. 252(12), 6214–6249 (2012)

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  18. Y. Enomoto, Y. Shibata, About compressible viscous fluid flow in a 2-Dimensional exterior domain, in Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, Operator Theory: Advances and Applications, vol. 221 (Birkhäuser/Springer Basel AG, Basel, 2012), pp. 305–321

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  19. Y. Enomoto, Y. Shibata, On the \(\mathcal{R}\)-sectoriality and the initial boundary value problem for the viscous compressible fluid flow. Funkcial. Ekvac. 56(3), 441–505 (2013)

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  20. Y. Enomoto, L. von Below, Y. Shibata, On some free boundary problem for a compressible barotropic viscous fluid flow. Ann. Univ. Ferrara Sez. VII Sci. Mat., 60(1), 55–89 (2014)

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  21. G.P. Galdi, J.G. Heywood, Y. Shibata, On the global existence and convergence to steady state of Navier–Stokes flow past an obstacle that is started from rest. Arch. Ration. Mech. Anal. 138(4), 307–318 (1997)

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  22. D. Gotz, Y. Shibata, On the \(\mathcal{R}\)-boundedness of the solution operators in the study of the compressible viscous fluid flow with free boundary conditions. Asymptot. Anal. 90(3–4), 207–236 (2014)

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  23. T. Hishida, Y. Shibata, Globally in time existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle. WSWAS Trans. Math. 5(3), 303–307 (2006)

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  24. T. Hishida, Y. Shibata, L p -L q estimate of the Stokes operator and Navier-Stokes flows in the exterior of a rotating obstacle. Arch. Ration. Mech. Anal. 193(2), 339–421 (2009)

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  25. M. Hieber, Y. Shibata, The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework. Math. Z. 265(2), 481–491 (2010)

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  26. H. Iwashita, Y. Shibata, On the analyticity of spectral functions for some exterior boundary value problems. Glasnik Math. Ser. III 23(43, 2), 291–313 (1988)

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  27. S. Kawashima, Y. Shibata, Global existence and exponential stability of small solutions to nonlinear viscoelasticity. Commun. Math. Phys. 148(1), 189–208 (1992)

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  28. S. Kawashima, Y. Shibata, On the Neumann problem of one–dimensional nonlinear thermoelasticity with time–independent external force. Czechoslovak Math. J. 45(120, 1), 39–67 (1995)

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  29. M. Kikuchi, Y. Shibata, On the mixed problem for some quasi–linear hyperbolic system with fully nonlinear boundary condition. J. Differ. Equ. 80(1), 154–197 (1989)

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  30. T. Kobayashi, H. Pecher, Y. Shibata, On a global in time existence theorem of smooth solutions to nonlinear wave equation with viscosity. Math. Ann. 296(2), 215–234 (1993)

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  31. T. Kobayashi, Y. Shibata, Exterior problems for the Navier-Stokes equations, in Nonlinear Evolution Equations and their Applications(Japanese) (913) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 1994/1995) pp. 185–190

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  32. T. Kobayashi, Y. Shibata, On the Oseen equation in exterior domains. Math. Ann. 310(1), 1–45 (1998)

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  33. T. Kobayashi, Y. Shibata, Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in R 3. Commun. Math. Phys. 200(3), 621–659 (1999)

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  34. T. Kobayashi, Y. Shibata, Remark on the rate of decay of solutions to linearized compressible Navier-Stokes equations. Pacific J. Math. 207(1), 199–234 (2002)

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  35. H. Kozono, Y. Shibata, Recent topics on mathematical theory of viscous incompressible fluid, in Lecture Notes in Numerical and Applied Analysis, vol. 16 (Kinokuniya, Tokyo, 1998)

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  36. T. Kubo, Y. Shibata, On some properties of solutions to the Stokes equation in the half-space and perturbed half-space, in Dispersive Nonlinear Problems in Mathematical Physics, Quad. Mat., Dept. Math., vol. 15 (Seconda Univ. Napoli, Caserta, 2004), pp. 149–220

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  37. T. Kubo, Y. Shibata, On the Stokes and Navier-Stokes equation in a perturbed half-space. Adv. Differ. Equ. 10(6), 695–720 (2005)

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  38. T. Kubo, Y. Shibata, On the Stokes and Navier-Stokes flows in a perturbed half space, in Regularity and Other Aspects of the Navier-Stokes Equations. Banach Center Publications vol. 70 (Polish Acad. Sci., Warsaw, 2005), pp. 157–167

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  39. T. Kubo, Y. Shibata, L p-L q estimate of the stokes semigroup and its application to navier-stokes equation in a perturbed half-space, in Hyperbolic Problems, Theory, Numerics and Applications II (Yokohama Publisher, Yokohama, 2006), pp. 125–132

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  40. T. Kubo, Y. Shibata, K. Soga, On the \(\mathcal{R}\)-boundedness for the two phase problem: compressible-incompressible model problem. Bound. Value Probl. 141, 33 pp. (2014)

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  41. J. Prüss, Y. Shibata, S. Shimizu, G. Simonett, On well-posedness of incompressible two-phase flows with phase transitions: the case of equal densities. Evol. Equ. Control Theory 1(1), 171–194 (2012)

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  42. A. Milani, Y. Shibata, On compatible regularizing data for second order hyperbolic initial–boundary value problems. Osaka J. Math 32(2), 347–362 (1995)

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  43. A. Milani, Y. Shibata, On the strong well–posedness of quasilinear hyperbolic initial–boundary value problems. Funkcial. Ekvaj. 38(3), 491–503 (1995)

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  44. J. Muñoz Rivera, Y. Shibata, A linear thermoelastic plate equation with Dirichlet boundary condition. Math. Methods Appl. Sci. 20(11), 915–932 (1997)

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  45. M. Murata, Y. Shibata, Lower bounds at infinity of solutions of partial differential equations in the exterior of a proper cone. Israel J. Math. 31(2), 193–203 (1978)

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  46. Y. Naito, Y. Shibata, On the L p analytic semigroup associated with the linear thermoelastic plate equations in the half-space. J. Math. Soc. Jpn. 61(4), 971–1011 (2009)

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  47. Y. Naito, R. Racke, Y. Shibata, Low frequency expansion in thermoelasticity with second sound in three dimensions. J. Math. Soc. Jpn. 62(4), 1289–1316 (2010)

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  48. G. Nakamura, Y. Shibata, On a local existence theorem for quasi–linear hyperbolic mixed problems with Neumann type boundary conditions, Proc. Japan Acad. Ser. A Math. Sci. 62(4), 117–120 (1986)

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  49. G. Nakamura, Y. Shibata, K. Tanuma, Whispering gallery waves in a neighborhood of a higher order zero of the curvature of the boundary. Publ. RIMS Kyoto Univ. 25(4), 605–629 (1989)

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  50. G. Nakamura, Y. Shibata, On a local existence theorem of Neumann problem for some quasi–linear hyperbolic systems of 2nd order. Math. Z. 202(1), 1–64 (1989)

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  51. M. Okamura, Y. Shibata, N. Yamaguchi, A Stokes approximation of two dimensional exterior Oseen flow near the boundary, in Asymptotic Analysis and Singularities–Hyperbolic and Dispersive PDEs and Fluid Mechanics. Advanced Studies in Pure Mathematics, vol. 47 (Mathematical Society, Tokyo, 2007), pp. 273–289

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  52. R. Racke, Y. Shibata, Global smooth solution and asymptotic stability in one-dimensional nonlinear thermoelasticity. Arch. Ration. Mech. Anal. 116(1), 1–34 (1991)

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  53. R. Racke, Y. Shibata, S. Mu Zheng, Global solvability and exponential stability in one–dimensional nonlinear thermoelasticity. Quart. Appl. Math. 51(4), 751–763 (1993)

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  54. H. Saito, Y. Shibata, On the Stokes equations with surface tension and gravity in \(\mathbb{R}_{+}^{N}\). J. Math. Soc. Jpn. (to appear)

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  55. Y. Shibata, A characterization of the hyperbolic mixed problems in a quarter space for differential operators with constant coefficients. Publ. RIMS Kyoto Univ. 15, 357–399 (1979)

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  56. Y. Shibata, Liouville type theorem for a system {P(D), B j (D), j = 1, …, p} of differential operators with constant coefficients in a half–space. Publ. RIMS Kyoto Univ. 16, 61–104 (1980)

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  57. Y. Shibata, \(\mathcal{E}\)–well posedness of mixed initial–boundary value problems with constant coefficients in a quarter space. J. D’Analyse Math. 37, 32–45 (1980)

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  58. Y. Shibata, \(\mathcal{E}\)–well posedness of mixed initial–boundary value problem with constant coefficients in a quarter– space II. Proc. Jpn. Acad. Ser. A. 56(7), 318–320 (1980)

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  59. Y. Shibata, Lower bounds at infinity of solutions of differential equations with constant coefficients in unbounded domains, in Singularities in Boundary Value Problems, ed. by H.G. Garnir. Proceedings of NATO Advanced Institute, Maratea, 1980. NATO Advanced Study Institute Series. Series C: Mathematical and Physical Sciences, vol. 65 (Reidel, Dordrecht, 1981), pp. 213–234

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  60. Y. Shibata, Lower bounds of solutions of general boundary value problems for differential operators with constant coefficients in a half–space, Japan. J. Math. (N.S.) 8(2), 343–382 (1982)

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  61. Y. Shibata, On the global existence of classical solutions of mixed problem for some second order non–linear hyperbolic operators with dissipative term in the interior domain. Funkcial. Ekvac. 25(3), 303–345 (1982)

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  62. Y. Shibata, On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain. Tsukuba J. Math. 7(1), 1–68 (1983)

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  63. Y. Shibata, On a local existence theorem for quasilinear hyperbolic mixed problems with Neumann type boundary conditions, in Hyperbolic Equations (Padua, 1985) Pitman Research Notes in Mathematics Series, vol. 158 (Longman Scientific & Technical, Harlow, 1987), pp. 282–286

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  64. Y. Shibata, On a local existence theorem of Neumann problem for some quasi–linear hyperbolic equations, in Calcul d’operateurs et fronts d’ondes, ed. by J. Vaillant, Travaux en Cours, vol. 29 (Hermann, Paris, 1988), pp. 133–167

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  65. Y. Shibata, On the Neumann problem for some linear hyperbolic systems of second order. Tsukuba J. Math. 12(1), 149–209 (1988)

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  66. Y. Shibata, On the Neumann problem for some linear hyperbolic systems of 2nd order with coefficients in Sobolev spaces. Tsukuba J. Math. 13(2), 283–352 (1989)

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  67. Y. Shibata, On one-dimensional nonlinear thermoelasticity, in Nonlinear Hyperbolic Equations and Field Theory (Lake Como, 1990), Pitmann Res. Notes Math. Ser., vol. 253 (Longman Scientific & Technical, Harlow, 1992), pp. 178–184

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  68. Y. Shibata, Neumann problem for one-dimensional nonlinear thermoelasticity, in Partial Differential Equations, Warsaw, 1990, Parts 1, 2, vol. 27 (Banach Center Publications/Polish Academy of Sciences, Warsaw, 1992), pp. 457–480

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  69. Y. Shibata, Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations. Comment. Math. Univ. Carol. 34(2), 295–312 (1993)

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  70. Y. Shibata, Neumann problem of one-dimensional nonlinear thermoelastic equations, in Mathematical Analysis of Phenomena in Fluid and Plasma Dynamics Kyoto, 1992. Surikaisekikenkyusho Kokyuroku (Japanese), vol. 824 (1993), pp. 283–296

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  71. Y. Shibata, On the exponential decay of the energy of a linear thermoelastic plate. Math. Appl. Comput. 13(2), 81–102 (1994)

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  72. Y. Shibata, Global in time existence of small solutions of nonlinear thermoviscoelastic equations. Math. Methods Appl. Sci. 18(11), 871–895 (1995)

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  73. Y. Shibata, On a linear thermoelastic plate equation, in Nonlinear Evolution Equations and Their Applications (898) (Japanese) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto,1993/1995), pp. 149–154

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  74. Y. Shibata, An initial-boundary value problem for some hyperbolic-parabolic coupled system, in Nonlinear Waves (Sapporo. 1995), GAKUTO International Series Mathematical Sciences Application, vol. 10 (Gakkōtosho, Tokyo, 1997), pp. 447–450

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  75. Y. Shibata, An exterior initial-boundary value problem for the Navier-Stokes equation, in Nonlinear waves (Sapporo, 1995), GAKUTO International Series Mathematical Sciences Application, vol. 10 (Gakkōtosho, Tokyo, 1997), pp. 431–446

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  76. Y. Shibata, On the decay estimate of the Stokes semigroup in a two dimensional exterior domain. Navier-Stokes Equations and Related Nonlinear Problems(Palanga, 1997) (VSP, Utrecht, 1998), pp. 315–330

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  77. Y. Shibata, On a Decay Rate of Solutions to One-Dimensional Thermoelastic Equations on a Half Line; Linear Part, ed. by S. Kawashima, T. Yanagisawa. Advances in Nonlinear Partial Differential Equations and Stochastics (World Scientific, Singapore, 1998), pp. 198–291

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  78. Y. Shibata, On an exterior initial-boundary value problem for Navier-Stokes equations. Quart. Appl. Math. 57(1), 117–155 (1999)

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  79. Y. Shibata, Global solutions of nonlinear evolution equations and their stability. Sūgaku, 51(1), 1–17 (1999) (in Japanese).

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  80. Y. Shibata, On the rate of decay of solutions to linear viscoelastic equation. Math. Methods Appl. Sci. 23(3), 203–226 (2000)

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  81. Y. Shibata, On a stability theorem of the Navier-Stokes equation in a three dimensional exterior domain, in Tosio Kato’s Method and Principle for Evolution Equations in Mathematical Physics, Sapporo, 2001 (1234) (Sūrikaisekikenkyūsho Kōkyūroku, 2001) pp. 146–172

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  82. Y. Shibata, On some stability theorems about viscous fluid flow, Quaderni del Seminario Matematico di Brescia (2003)

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  83. Y. Shibata, Time-global solutions of nonlinear evolution equations and their stability [translation of Sūgaku 51(1), 1–17 (1999)], in Selected Papers on Analysis and Differential Equations. American Mathematical Society Translations: Series 2, vol. 211 (American Mathematical Society, Providence, RI, 2003), pp. 87–105

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  84. Y. Shibata, On some stability theorem of the steady flow of compressible viscous fluid with respect to the initial disturbance, in Hyperbolic Problems and Related Topics, Graduate Series Analysis (International Press, Somerville, MA, 2003), pp. 341–357

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  85. Y. Shibata, On the Oseen semigroup with rotating effect. in Functional Analysis and Evolution Equations (Birkhäuser, Basel, 2008), pp. 595–611

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  86. Y. Shibata, A stability theorem of the Navier-Stokes flow past a rotating body. in Parabolic and Navier-Stokes Equations. Part 2, vol. 81 (Banach Center Publication, Polish Academy of Science Institute of Mathematics, Warsaw, 2008), pp. 441–455

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  87. Y. Shibata, On a C 0 semigroup associated with a modified Oseen equation with rotating effect, in Advances in Mathematical Fluid Mechanics, (Springer, Berlin, 2010), pp. 513–551

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  88. Y. Shibata, Generalized resolvent estimates of the Stokes equations with first order boundary condition in a general domain. J. Math. Fluid Mech. 15(1), 1–40 (2013)

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  89. Y. Shibata, On the \(\mathcal{R}\)-boundedness of solution operators for the weak Dirichlet-Neumann problem, in RIMS Kōkyūroku 1875, Mathematical Analysis of Incompressible Flow (4–6 Feb 2013), ed. by T. Hishida (RIMS, Kyoto University, Kyoto), pp. 1–18

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  90. Y. Shibata, On the \(\mathcal{R}\)-boundedness of solution operators for the Stokes equations with free boundary condition. Differ. Integr. Equ. 27(3–4), 313–368 (2014)

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  91. Y. Shibata, On some free boundary problem of the Navier-Stokes equations in the maximal L p -L q regularity class. J. Differ. Equ. 258, 4127–4155 (2015)

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  92. Y. Shibata, On the global well-posedness of some free boundary problem for a compressible barotropic viscous fluid flow, in The Contemporary Mathematics Series of the American Mathematical Society: Recent Advances in PDEs and Applications, Levico Terme, 17–21 February 2014 [to celebrate the 70th Birthday of Professor Hugo Beirao da Veiga]

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  93. Y. Shibata, Local well-posedness of compressible-incompressible two-phase flows with phase transitions, To appear in the Proceedings of Levico Conf. on fluid Dyn and Electromagnetism. arXiv:submit/1156284 [math. AP] 10 Jan 2015

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  94. Y. Shibata, On the \(\mathcal{R}\)-boundedness for the two phase problem with phase transition: compressible-incompressible model problem. Funk. Ekvaj. (to appear)

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  95. Y. Shibata, W. Dan, On a local energy decay of solutions of a dissipative wave equation, inMathematical Analysis of Phenomena in Fluid and Plasma Dynamics (Japanese) (862) (Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 1993/1994) pp. 181–190

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  96. Y. Shibata, S. Mu Zheng, On some nonlinear hyperbolic system with damping boundary condition. Nonlinear Anal. TMA 17(3), 233–266 (1991)

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  97. Y. Shibata, Y. Tsutsumi, Global existence theorem for nonlinear wave equations in exterior domain, in Recent Topics in Nonlinear PDE (Hiroshima, 1983), North-Holland Mathematics Studies vol. 98 (North-Holland, Amsterdam, 1984) pp. 155–196

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  98. Y. Shibata, Y. Tsutsumi, Global existence theorem for nonlinear wave equation in exterior domain. Proc. Japan Acad. A Mat. Sci. 60(1), 14–17 (1984)

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, 8057, Zürich, Switzerland

    Herbert Amann

  2. Graduate School of Mathematical Sciences, University of Tokyo, 153-8914, Tokyo, Japan

    Yoshikazu Giga

  3. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Hisashi Okamoto

  4. Department of Mathematics, Waseda University, Tokyo, 169-8555, Japan

    Hideo Kozono & Masaso Yamazaki

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  1. Herbert Amann
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  2. Yoshikazu Giga
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  3. Hisashi Okamoto
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  4. Hideo Kozono
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  5. Masaso Yamazaki
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Correspondence to Hideo Kozono .

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  1. Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

    Herbert Amann

  2. University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

    Yoshikazu Giga

  3. Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono

  4. Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

    Hisashi Okamoto

  5. Department of Mathematics, Waseda University, Tokyo, Japan

    Masao Yamazaki

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Amann, H., Giga, Y., Okamoto, H., Kozono, H., Yamazaki, M. (2016). The Work of Yoshihiro Shibata. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_1

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