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

Hongjun Gao; Chengfeng  Sun

doi:10.3934/dcdsb.2016087

Article Contents

2016, Volume 21, Issue 9: 3053-3073. Doi: 10.3934/dcdsb.2016087

This issue Previous Article Mean field limit with proliferation Next Article Semilinear stochastic equations with bilinear fractional noise

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

Hongjun Gao^1, and
Chengfeng Sun^2,

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

Received: November 2015

Revised: February 2016

Published: November 2016

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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.

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Mathematics Subject Classification: 35Q99, 60H15, 76M35, 86A05, 86A10.

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