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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 Stokesequations, based on the approach of Von Wahl, for the deterministic case. Wepresent several approaches of the concept, depending on the smoothnessavailable. When smoothness is available, we can in someway reduce thestochastic equation to a deterministic one with a random parameter. In thegeneral case, we mimic the concept of local solution for stochasticdifferential equations.

Keywords

Navier Stokes equationsstochastic equationsabstract parabolic equationsIto integrallocal solutionIto equationStokes operatorFunctionalequationMild solutionRandom time.

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References

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