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Local Solutions for Stochastic Navier Stokes Equations

Published online by Cambridge University Press:  15 April 2002

Alain Bensoussan  and
Jens Frehse
Alain Bensoussan
Affiliation:
University Paris Dauphine and CNES, 2 Place Maurice Quantor, 75001 Paris, France.
Jens Frehse
Affiliation:
Institüt für Angewandte Mathematik, Universität Bonn, 6 BeringStrasse, Bonn, Germany.
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Abstract

In this article we consider local solutions for stochastic Navier Stokes equations, based on the approach of Von Wahl, for the deterministic case. We present several approaches of the concept, depending on the smoothness available. When smoothness is available, we can in someway reduce the stochastic equation to a deterministic one with a random parameter. In the general case, we mimic the concept of local solution for stochastic differential equations.

Keywords

Navier Stokes equationsstochastic equationsabstract parabolic equationsIto integrallocal solutionIto equationStokes operatorFunctional equationMild solutionRandom time.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 241 - 273
Copyright
© EDP Sciences, SMAI, 2000

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References

Bensoussan, A., Stochastic Navier Stokes Equations. Acta Appl. Math. 38 (1995) 267-304. CrossRef
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