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 - <p style="text-align: justify;">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.</p>