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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Leslie, T. M.¹  Shvydkoy, R.¹ 

[1] Univ Illinois, Chicago, IL 60607 USA

关键词: Navier-Stokes equation;    Onsager conjecture;    Karman-Howarth-Monin relation;    Turbulence;   

DOI  :  10.1016/j.jde.2016.06.001

来源: Elsevier

【 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.

【 授权许可】

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