Local Solutions for Stochastic Navier Stokes Equations
University Paris Dauphine and CNES, 2 Place Maurice Quantor,
75001 Paris, France.
2 Institüt für Angewandte Mathematik, Universität Bonn, 6 BeringStrasse, Bonn, Germany.
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.
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