On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum  

作　　者：Xiangdi Huang 

机构地区：[1]Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2021年第8期1771-1788,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11688101,11731007 and 11671412);Youth Innovation Promotion Association,Chinese Academy of Sciences。

摘　　要：We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density containing vacuum initially.We first prove the local existence and uniqueness of the strong solutions,where the initial compatibility condition proposed by Cho et al.(2004),Cho and Kim(2006)and Choe and Kim(2003)is removed in a suitable sense.Then the continuous dependence of strong solutions on the initial data is derived under an additional compatibility condition.Moreover,for the initial data satisfying some additional regularity and the compatibility condition,the strong solution is proved to be a classical one.

关 键 词：compressible Navier-Stokes equations VACUUM strong solutions classical solutions 

分 类 号：O175[理学—数学]