Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity  

作　　者：ZHANG Ting FANG Dao-yuan 

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

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第10期1681-1690,共10页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project supported by the National Natural Science Foundation of China (No. 10571158) and the DFG

摘　　要：We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential re- quirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential requirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc^1-norm of the velocity gradient is locally integrable in time.

关 键 词：Compressible Navier-Stokes equations Vacuum states Density-dependent viscosity 

分 类 号：O175[理学—数学]