We consider the Stokes approximation equations for compressible flows in /~3. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a cons...We consider the Stokes approximation equations for compressible flows in /~3. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As an imme- diate byproduct, the usual Lp - L2（1 〈 p 〈 2） type of the optimal decay rate follow without requiring that the Lp norm of initial data is small.展开更多
In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.
基金Supported by National Natural Science Foundation of China(11271305,11161011)Science and Technology Foundation of Guizhou Province of China(LKS[2012]11,LKS[2013]03,LKS[2013]05)
文摘We consider the Stokes approximation equations for compressible flows in /~3. The global unique solution and optimal convergence rates are obtained by pure energy method provided the initial perturbation around a constant state is small. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As an imme- diate byproduct, the usual Lp - L2（1 〈 p 〈 2） type of the optimal decay rate follow without requiring that the Lp norm of initial data is small.
基金A The research is supported in part by the National Natural Science Foundation of China （Grant No. 10401012） and The Project Sponsored by the Scientific Research Foundation for the Returned 0verseas Chinese Scholars, State Education Ministry.Acknowledgment This is a part of my Ph.D thesis at The Institute of Mathematical Sciences, The Chinese University of Hong Kong. I express my deep gratitude to my graduate advisor, Professor Zhouping Xin, for his guidance and encouragement.
文摘In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.
