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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.
}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0010}, url = {http://global-sci.org/intro/article_detail/aam/23422.html} }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.