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arXiv · 1512.05674

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

Peter Constantin·Tarek Elgindi·Mihaela Ignatova·Vlad Vicol
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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.

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Peter Constantin, Tarek Elgindi, Mihaela Ignatova, Vlad Vicol. 2016-06-21. Remarks on the inviscid limit for the Navier-Stokes equations for uniformly bounded velocity fields. https://arxiv.org/abs/1512.05674

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