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| Energy Equality for the IsentropicCompressible Navier-Stokes Equationswithout Upper Bound of the Density |
| Yulin Ye,Yanqing Wang,Huan Yu |
| (School of Mathematics and Statistics, Henan University, Kaifeng,
Henan 475004, China;College of Mathematics and Information Science, Zhengzhou University
of Light Industry, Zhengzhou, Henan 450002, China;School of Applied Science, Beijing Information Science and Technology
University, Beijing 100192, China) |
| DOI： |
| 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 ρ 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. |
| Key words: Compressible Navier-Stokes equations, energy equality, vacuum. |