Abstract
The main object of our investigation is the system of stochastic Navier-Stokes equations considered in a bounded domain D in ℝn with boundary of class C 2. The vector u = (u 1, ⋯, u n ) represents the velocity of a fluid, v is the viscosity coefficient, (f i ) is the vector of external forces, p represents the pressure, is white noise. Functions with vanishing divergence are called solenoidal. This condition corresponds to the fact that the fluid is incompressible.
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References
Capiński, M. and Cutland, N.J., (1992) A simple proof of existence of weak and statistical solutions of Navier-Stokes equations, Proceedings of the Royal Society, London, Ser. A, 436, pp. 1–11.
Capinski, M. and Cutland, N.J., (1995) Nonstandard Methods for Stochastic Hydromechanics, World Scientific, Singapore.
Ichikawa, A., (1982) Stability of semilinear stochastic evolution equations, Journal of Mathematical Analysis and Applications 90, pp. 12–44.
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© 1997 Springer Science+Business Media Dordrecht
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Capiński, M. (1997). A Nonstandard Approach to Hydromechanics. In: Arkeryd, L.O., Cutland, N.J., Henson, C.W. (eds) Nonstandard Analysis. NATO ASI Series, vol 493. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5544-1_12
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DOI: https://doi.org/10.1007/978-94-011-5544-1_12
Publisher Name: Springer, Dordrecht
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