The stochastic primitive equations in two space dimensions with multiplicative noise

Nathan Glatt-Holtz; Mohammed Ziane

doi:10.3934/dcdsb.2008.10.801

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2008, Volume 10, Issue 4: 801-822. Doi: 10.3934/dcdsb.2008.10.801

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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

Received: July 31, 2007

Revised: February 29, 2008

Published: August 2008

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Abstract

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:

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

Mathematics Subject Classification: Primary: 76D03, 60H15; Secondary: 37L65.

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