The energy balance relation for weak solutions of the density-dependent Navier-Stokes equations

被引：31

作者：

Leslie, T. M. ^{[1
]}

Shvydkoy, R. ^{[1
]}

机构：

[1] Univ Illinois, Chicago, IL 60607 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 06期

基金：

美国国家科学基金会;

关键词：

Navier-Stokes equation; Onsager conjecture; Karman-Howarth-Monin relation; Turbulence; EULER EQUATIONS; CONSERVATION; DISSIPATION; CONJECTURE;

D O I：

10.1016/j.jde.2016.06.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance relation for this system holds for weak solutions if the velocity, density, and pressure belong to a range of Besov spaces of smoothness 1/3. A density-dependent version of the classical Karman-Howarth-Monin relation is derived. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：3719 / 3733

页数：15

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