Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Peter Constantin; Tarek Elgindi; Mihaela Ignatova; Vlad Vicol

Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Analysis of PDEs 2016-06-23 v3

Authors: Peter Constantin , Tarek Elgindi , Mihaela Ignatova , Vlad Vicol

Abstract

We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes solutions are equicontinuous at $x_2=0$ . A sufficient condition for this to hold is that the tangential Navier-Stokes velocity remains uniformly bounded and has a uniformly integrable tangential gradient near the boundary.

Keywords

inviscid limit Navier-Stokes equations vanishing viscosity half space Dirichlet boundary conditions energy norm equicontinuity

Cite

@article{arxiv.1512.05674,
  title  = {Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields},
  author = {Peter Constantin and Tarek Elgindi and Mihaela Ignatova and Vlad Vicol},
  journal= {arXiv preprint arXiv:1512.05674},
  year   = {2016}
}

Comments

We thank Gung-Min Gie and Jim Kelliher for many useful comments about the paper, which are incorporated in this new version

Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields

Abstract

Keywords

Cite

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