THE CAUCHY PROBLEM FOR NONHOMOGENEOUS NAVIER-STOKES EQUATIONS IN L^q([0,T];L^p)  

作　　者：苗长兴 顾永耕 

出　　处：《Acta Mathematicae Applicatae Sinica》1999年第2期163-171,共9页应用数学学报（英文版）

摘　　要：In this paper the Cauchy problem for a class of nonhomogenous Navier-Stokes equationsin the infinite cylinder is considered. We construct a unique local solution infor a class of nonhomogeneous Navier-Stokes equations provided that initialdata are in, where is an exponent determined by the structure of nonlinear termsand p,q are such that . Meanwhile under suitable conditions we also obtain thatprovided that initial data are sufficiently small.In this paper the Cauchy problem for a class of nonhomogenous Navier-Stokes equationsin the infinite cylinder is considered. We construct a unique local solution infor a class of nonhomogeneous Navier-Stokes equations provided that initialdata are in, where is an exponent determined by the structure of nonlinear termsand p,q are such that . Meanwhile under suitable conditions we also obtain thatprovided that initial data are sufficiently small.

关 键 词：Admissible triple Navier-Stokes equations Cauchy problem space-time estimates 

分 类 号：O175[理学—数学]