The Energy Balance Relation for Weak solutions of the Density-Dependent\n Navier-Stokes Equations

2016/02/26 by Trevor M. Leslie, Leslie, Trevor, Roman Shvydkoy +1 · 2 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1602.08527

Abstract

We consider the incompressible inhomogeneous Navier-Stokes equations with\nconstant viscosity coefficient and density which is bounded and bounded away\nfrom zero. We show that the energy balance relation for this system holds for\nweak solutions if the velocity, density, and pressure belong to a range Besov\nspaces of smoothness 1/3. A density-dependent version of the classical\nK 'arm 'an-Howarth-Monin relation is derived.\n

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