Wellposedness for anisotropic rotating fluid equations  

作　　者：FANG Dao-yuan WANG Su-mei ZHANG Ting 

机构地区：[1]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第1期9-33,共25页高校应用数学学报（英文版）（B辑）

基　　金：Supported by NSFC(10871175,10931007,10901137);Zhejiang Provincial Natural Science Foundation of China(Z6100217);Program for New Century Excellent Talents in University

摘　　要：The weUposedness problem for an anisotropic incompressible viscous fluid in R3, ro- tating around a vector B（t, x） ：= （b1 （t, x）, b2 （t, x）, b3 （t, x））, is studied. The global wellposedness in the homogeneous case （B = e3） with sufficiently fast rotation in the space B0,1/2 is proved. In the inhomogeneous case （B = B（t, xh））, the global existence and uniqueness of the solution in B0,1/2 are obtained, provided that the initial data are sufficient small compared to the horizontal viscosity. Furthermore, we obtain uniform local existence and uniqueness of the solution in the x same function space. We also obtain propagation of the regularity in B2,11/2 under the additional assumption that B depends only on one horizontal space variable.The weUposedness problem for an anisotropic incompressible viscous fluid in R3, ro- tating around a vector B（t, x） ：= （b1 （t, x）, b2 （t, x）, b3 （t, x））, is studied. The global wellposedness in the homogeneous case （B = e3） with sufficiently fast rotation in the space B0,1/2 is proved. In the inhomogeneous case （B = B（t, xh））, the global existence and uniqueness of the solution in B0,1/2 are obtained, provided that the initial data are sufficient small compared to the horizontal viscosity. Furthermore, we obtain uniform local existence and uniqueness of the solution in the x same function space. We also obtain propagation of the regularity in B2,11/2 under the additional assumption that B depends only on one horizontal space variable.

关 键 词：the anisotropic Navier-Stokes-Coriolis equation WELLPOSEDNESS anisotropic. 

分 类 号：O343.8[理学—固体力学] O175.29[理学—力学]