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

Trevor Leslie; Roman Shvydkoy

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

Analysis of PDEs 2016-03-01 v1

Authors: Trevor Leslie , Roman Shvydkoy

Abstract

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 Besov spaces of smoothness $1/3$ . A density-dependent version of the classical K\'arm\'an-Howarth-Monin relation is derived.

Keywords

density-dependent navier-stokes equations weak solutions energy balance relation besov spaces kármán-howarth-monin relation inhomogeneous density constant viscosity

Cite

@article{arxiv.1602.08527,
  title  = {The Energy Balance Relation for Weak solutions of the Density-Dependent Navier-Stokes Equations},
  author = {Trevor Leslie and Roman Shvydkoy},
  journal= {arXiv preprint arXiv:1602.08527},
  year   = {2016}
}

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12 pages

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