Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Stochastic 2-D Navier-Stokes Equation

Journal Article · · Applied Mathematics and Optimization
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 significantly 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.
OSTI ID:
21064247
Journal Information:
Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 46; ISSN 0095-4616
Country of Publication:
United States
Language:
English

Similar Records

Deterministic and Stochastic Control of Navier-Stokes Equation with Linear, Monotone, and Hyperviscosities
Journal Article · Tue Mar 14 23:00:00 EST 2000 · Applied Mathematics and Optimization · OSTI ID:21064274

Existence and Regularity of the Pressure for the Stochastic Navier-Stokes Equations
Journal Article · Wed Oct 15 00:00:00 EDT 2003 · Applied Mathematics and Optimization · OSTI ID:21064229

Optimal Control for Two-Dimensional Stochastic Navier-Stokes Equations
Journal Article · Sun Jan 14 23:00:00 EST 2007 · Applied Mathematics and Optimization · OSTI ID:21064196