THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA  

作　　者：王海涛 张雄韬 Haitao WANG;Xiongtao ZHANG(Institute of Natural Sciences and School of Mathematical Sciences,LSC-MOE,Shanghai Jiao Tong University,Shanghai 200240,China;School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]Institute of Natural Sciences and School of Mathematical Sciences,LSC-MOE,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China

出　　处：《Acta Mathematica Scientia》2023年第4期1675-1716,共42页数学物理学报（B辑英文版）

基　　金：partially the National Key R&D Program of China(2022YFA1007300);the NSFC(11901386,12031013);the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA25010403);the NSFC(11801194,11971188);the Hubei Key Laboratory of Engineering Modeling and Scientific Computing。

摘　　要：A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.

关 键 词：compressible Navier-Stokes equation BV initial data REGULARITY UNIQUENESS 

分 类 号：O175[理学—数学]