Volume 40, Issue 3
Energy Equality for the Isentropic Compressible Navier-Stokes Equations Without Upper Bound of the Density

Yulin Ye, Yanqing Wang & Huan Yu

Ann. Appl. Math., 40 (2024), pp. 285-313.

Published online: 2024-09

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  • 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.

  • AMS Subject Headings

35Q30, 35Q35, 76N06, 76N10

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COPYRIGHT: © Global Science Press

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@Article{AAM-40-285, author = {Ye , YulinWang , Yanqing and Yu , Huan}, title = {Energy Equality for the Isentropic Compressible Navier-Stokes Equations Without Upper Bound of the Density}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {3}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0010}, url = {http://global-sci.org/intro/article_detail/aam/23422.html} }
TY - JOUR T1 - Energy Equality for the Isentropic Compressible Navier-Stokes Equations Without Upper Bound of the Density AU - Ye , Yulin AU - Wang , Yanqing AU - Yu , Huan JO - Annals of Applied Mathematics VL - 3 SP - 285 EP - 313 PY - 2024 DA - 2024/09 SN - 40 DO - http://doi.org/10.4208/aam.OA-2024-0010 UR - https://global-sci.org/intro/article_detail/aam/23422.html KW - Compressible Navier-Stokes equations, energy equality, vacuum. AB -

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.

Ye , YulinWang , Yanqing and Yu , Huan. (2024). Energy Equality for the Isentropic Compressible Navier-Stokes Equations Without Upper Bound of the Density. Annals of Applied Mathematics. 40 (3). 285-313. doi:10.4208/aam.OA-2024-0010
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