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Energy Equality for the Isentropic Compressible Navier-Stokes Equations without Upper Bound of the Density
Yulin Ye, Yanqing Wang and Huan Yu

Ann. Appl. Math. DOI: 10.4208/aam.OA-2024-0010

Publication Date : 2024-09-02

  • Abstract

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 density $\rho$ means that more integrability of  the velocity $v$ or the gradient  of the velocity  $\nabla v$ are necessary for energy conservation of the  isentropic compressible fluid and the inverse is also true.


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