Affiliation:
1. Center for Mathematical Sciences, School of Science, Wuhan University of Technology, Wuhan 430070, China
Abstract
In this article, two classes of sufficient conditions of weak solutions are given to guarantee the energy conservation of the compressible Euler equations. Our strategy is to introduce a test function φ(t)vϵ to derive the total energy. The velocity field v needs to be regularized both in time and space. In contrast to the noncompressible Euler equations, the compressible flows we consider here do not have a divergence-free structure. Therefore, it is necessary to make an additional estimate of the pressure p, which takes advantage of an appropriate commutator. In addition, by using the weak convergence, we show that the energy equality is conserved in a point-wise sense.
Funder
NSFC
Fundamental Research Funds for the Central University
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
1 articles.
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