Stochastic 2-D Navier-Stokes Equation

Authors

J. L. Menaldi, Wayne State UniversityFollow
S. S. Sritharan, United States Navy

Document Type

Article

Abstract

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.

Disciplines

Analysis | Probability

Comments

The final publication is available at Springer via https://dx.doi.org/10.1007/s00245-002-0734-6

Recommended Citation

Menaldi & Sritharan Appl Math Optim (2002) 46: 31. doi: 10.1007/s00245-002-0734-6