Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Well-posedness of stochastic primitive equations with multiplicative noise in three dimensions

Pages: 3053 - 3073, Volume 21, Issue 9, November 2016      doi:10.3934/dcdsb.2016087

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Hongjun Gao - Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China (email)
Chengfeng Sun - Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China (email)

Abstract: Three dimensional primitive equations with a small multiplicative noise are studied in this paper. The existence and uniqueness of solutions with small initial value in a fixed probability space are obtained. The proof is based on Galerkin approximation, Itô's formula and weak convergence methods.

Keywords:  Primitive equation, Galerkin approximations, Itô's formula, existence, uniqueness.
Mathematics Subject Classification:  35Q99, 60H15, 76M35, 86A05, 86A10.

Received: November 2015;      Revised: February 2016;      Available Online: October 2016.