ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION  

作　　者：蒲学科 周文利 Xueke PU;Wenli ZHOU(School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China)

机构地区：[1]School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China

出　　处：《Acta Mathematica Scientia》2023年第3期1081-1104,共24页数学物理学报（B辑英文版）

基　　金：Pu was supported in part by the NNSF of China(11871172);the Science and Technology Projects in Guangzhou (202201020132);Zhou was supported by the Innovation Research for the Postgraduates of Guangzhou University (2021GDJC-D09)。

摘　　要：In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.

关 键 词：Boussinesq equations primitive equations density stratification hydrostatic approximation strong convergence 

分 类 号：O35[理学—流体力学]