Energy Equality for the Isentropic Compressible Navier-Stokes Equations Without Upper Bound of the Density
Year: 2024
Author: Yulin Ye, Yanqing Wang, Huan Yu
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 285–313
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 $∇v$ are necessary for energy conservation of the isentropic compressible fluid and the inverse is also true.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0010
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 285–313
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Compressible Navier-Stokes equations energy equality vacuum.