# American Institute of Mathematical Sciences

November  2016, 21(9): 3053-3073. doi: 10.3934/dcdsb.2016087

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

 1 Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Science, Nanjing Normal University, Nanjing 210023 2 Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China

Received  November 2015 Revised  February 2016 Published  October 2016

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.
Citation: Hongjun Gao, Chengfeng Sun. Well-posedness of stochastic primitive equations with multiplicative noise in three dimensions. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3053-3073. doi: 10.3934/dcdsb.2016087
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