| Issue |
ESAIM: M2AN
Volume 34, Number 2, March/April 2000
Special issue for R. Teman's 60th birthday
|
|
|---|---|---|
| Page(s) | 241 - 273 | |
| DOI | https://doi.org/10.1051/m2an:2000140 | |
| Published online | 15 April 2002 | |
Local Solutions for Stochastic Navier Stokes Equations
1
University Paris Dauphine and CNES, 2 Place Maurice Quantor,
75001 Paris, France.
2
Institüt für Angewandte Mathematik, Universität
Bonn, 6 BeringStrasse, Bonn, Germany.
Received:
2
December
1999
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.
Mathematics Subject Classification: 35Q30 / 76D06
Key words: Navier Stokes equations / stochastic equations / abstract parabolic equations / Ito integral / local solution / Ito equation / Stokes operator / Functional equation / Mild solution / Random time.
© EDP Sciences, SMAI, 2000
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