Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications(Dedicated to Haim Brézis on the occasion of his 70th birthday)

作     者：Nathan GLATT-HOLTZ Roger TEMAM Chuntian WANG 

作者机构：department of mathematicstulane universityLA 70118USA department of mathematics and the institute for scientific computing and applied mathematicsindiana universityBloomingtonIN 47405USA department of mathematicsuniversity of los angelesCA 90059USA 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2017年第38卷第2期

页      面：425-472页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Science Foundation under the grants NSF-DMS-1206438 and NSF-DHS-1510249,the National Science Foundation under the grants NSF-DMS-1004638 and NSF-DMS-1313272 the Research Fund of Indiana University 

主　　题：Nonlinear stochastic partial differential equations, Geophysical fluid dy-namics, Primitive equations, Discrete time approximation, Martingalesolutions~ Numerical analysis of stochastic PDEs 

摘      要：As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and the oceans, the time discretization of these equations by an implicit Euler scheme is studied. From the deterministic point of view, the 3D primitive equations are studied in their full form on a general domain and with physically realistic boundary conditions. From the probabilistic viewpoint, this paper deals with a wide class of nonlinear, state dependent, white noise forcings which may be interpreted in either the Itor the Stratonovich sense. The proof of convergence of the Euler scheme,which is carried out within an abstract framework, covers the equations for the oceans, the atmosphere, the coupled oceanic-atmospheric system as well as other related geophysical equations. The authors obtain the existence of solutions which are weak in both the PDE and probabilistic sense, a result which is new by itself to the best of our knowledge.