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Full-Text Articles in Analysis
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan
Mathematics Faculty Research Publications
In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.