The stochastic primitive equations in two space dimensions with multiplicative noise

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September 2008, 10(4): 801-822. doi: 10.3934/dcdsb.2008.10.801

The stochastic primitive equations in two space dimensions with multiplicative noise

Nathan Glatt-Holtz ^1, and Mohammed Ziane ^1,

1.	Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States, United States

Received August 2007 Revised March 2008 Published August 2008

Abstract
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We study the two dimensional primitive equations in the presence of multiplicative stochastic forcing. We prove the existence and uniqueness of solutions in a fixed probability space. The proof is based on finite dimensional approximations, anisotropic Sobolev estimates, and weak convergence methods.

Keywords: Stochastic Partial Differential Equations, Primitive Equations, Existence and Uniqueness., Galerkin Approximation, Geophysical Fluid Dynamics.

Mathematics Subject Classification: Primary: 76D03, 60H15; Secondary: 37L6.

Citation: Nathan Glatt-Holtz, Mohammed Ziane. The stochastic primitive equations in two space dimensions with multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 801-822. doi: 10.3934/dcdsb.2008.10.801

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