非齐次不可压与可压 Euler 方程的能量守恒
偏微分方程分析
2019-09-23 v3
摘要
在环面或有界域中，研究了具有一般压力律的非齐次不可压与可压 Euler 方程的能量守恒。我们给出了弱解守恒能量的充分条件。通过利用合适的检验函数，不可压情形中密度仅需 阶空间正则性，可压情形中仅需 阶。当密度为常量时，我们恢复了经典不可压 Euler 方程的已有结果。
引用
@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}
}
备注
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