Energy Equality for the Isentropic Compressible Navier-Stokes Equations without Upper Bound of the Density  

作　　者：Yulin Ye Yanqing Wang Huan Yu 

机构地区：[1]School of Mathematics and Statistics,Henan University,Kaifeng,Henan 475004,China [2]College of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou,Henan 450002,China [3]School of Applied Science,Beijing Information Science and Technology University,Beijing 100192,China

出　　处：《Annals of Applied Mathematics》2024年第3期285-313,共29页应用数学年刊（英文版）

基　　金：partially supported by the National Natural Science Foundation of China under grant(No.11701145);the Natural Science Foundation of Henan Province(No.232300420111);the Training Plan for Young Backbone Teachers in Colleges and Universities of Henan Province(No.2024GGJS022);partially supported by the National Natural Science Foundation of China under grant(Nos.1971446,12071113 and 11601492);sponsored by Natural Science Foundation of Henan(No.232300421077);partially supported by the National Natural Science Foundation of China(NNSFC)(No.11901040);Beijing Natural Science Foundation(BNSF)(No.1204030);Beijing Municipal Education Commission(KM202011232020)。

摘　　要：In this paper,we are concerned with the minimal regularity of both the density and the velocity for the weak solutions keeping energy equality in the isentropic compressible Navier-Stokes equations.The energy equality criteria without upper bound of the density are established for the first time.Our results imply that the lower integrability of the densityρmeans that more integrability of the velocity v or the gradient of the velocity?v are necessary for energy conservation of the isentropic compressible fluid and the inverse is also true.

关 键 词：Compressible Navier-Stokes equations energy equality VACUUM 

分 类 号：O175[理学—数学]