Energy conservation for inhomogeneous incompressible and compressible Euler equations
Abstract
Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By exploiting a suitable test function, the spatial regularity for the density is only required to be of order in the incompressible case, and of order in the compressible case. When the density is constant, we recover the existing results for classical incompressible Euler equation.
Keywords
Cite
@article{arxiv.1808.10297,
title = {Energy conservation for inhomogeneous incompressible and compressible Euler equations},
author = {Quoc-Hung Nguyen and Phuoc-Tai Nguyen and Bao Quoc Tang},
journal= {arXiv preprint arXiv:1808.10297},
year = {2019}
}
Comments
The new version deals with general pressure law for compressible equations. By using a new test function, we allow the density to be zero instead of excluding completely vacuum. Required regularities for the density in the compressible case are also reduced