Energy conservation of the compressible Euler equations and the Navier-Stokes equations via the gradient

被引：2
|
作者：
Ye, Yulin [1 ]
Guo, Peixian [1 ]
Wang, Yanqing [2 ]
机构：
[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China
[2] Zhengzhou Univ Light Ind, Coll Math & Informat Sci, Zhengzhou 450002, Henan, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 230卷
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Compressible Euler equations; Compressible Navier-Stokes; equations; Energy conservation; Vacuum; WEAK SOLUTIONS; CONJECTURE;
D O I：
10.1016/j.na.2023.113219
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we derive a sufficient condition keeping energy conservation in terms of the gradient of the velocity for the weak solutions of the compressible Euler equations for both the non-vacuum and the vacuum cases. As a by-product, this result is also true for the energy conservation of weak solutions to compressible Navier-Stokes equations allowing vacuum, which can be viewed as an affirmative answer to the question posed by Liang in [ Proc. Roy. Soc. Edinburgh Sect. A, (2020)].(c) 2023 Elsevier Ltd. All rights reserved.
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页数：18
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