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Large Time Behavior of the Navier–Stokes Flow

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

Different results related to the asymptotic behavior of incompressible fluid equations are analyzed as time tends to infinity. The main focus is on the solutions to the Navier–Stokes equations, but in the final section, a brief discussion is added on solutions to magnetohydrodynamics, liquid crystals, and quasi-geostrophic and Boussinesq equations. Consideration is given to results on decay, asymptotic profiles, and stability for finite and nonfinite energy solutions.

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Part I. Incompressible fluids. Unsteady viscous Newtonian fluids. Yoshikazu Giga and Antonn Novotný editors. Springer L. Brandolese is supported by the ANR project DYFICOLTI N. 36338

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Acknowledgements

The authors thank the anonymous reviewers for some very helpful suggestions and corrections which served to improve the presentation of this chapter.

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  1. Institut Camille Jordan, Université Lyon 1, 21, avenue Claude Bernand, 69622, Villeurbanne, France

    Lorenzo Brandolese

  2. Department of Mathematics, University of California Santa Cruz, 95064, Santa Cruz, CA, USA

    Maria E. Schonbek

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    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Brandolese, L., Schonbek, M. (2016). Large Time Behavior of the Navier–Stokes Flow. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_11-1

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