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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

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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