Energy conservation for weak solutions to the pressureless Euler-Navier-Stokes system in three-dimensional space

被引：1

作者：

Chen, Senming ^{[1
]}

机构：

[1] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 04期

基金：

中国国家自然科学基金;

关键词：

energy conservation; Euler equation; Navier-Stokes equations; weak solutions; INCOMPRESSIBLE EULER; DISSIPATION; CONJECTURE; ONSAGER;

D O I：

10.1002/mma.9725

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the energy conservation for the weak solution of the 3D Euler-Navier-Stokes system. we provide two sufficient conditions on the regularity of weak solutions to guarantee the conservation of total energy, which also including the initial energy. Due to the couple structure between inhomogeneous Euler equation and incompressible Navier-Stokes system, we adopt a variant of the method from R. Chen and C. Yu (J. Math. Pures Appl. 131 (2019), 1-16.) and J. Lions (Rend. Semin. Mat. Univ. Padova 30 (1960), 16-23.) to deal with the density of Euler flows and velocity of Navier-Stokes fluid.

引用

页码：1903 / 1914

页数：12

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