Vanishing viscosity in the plane for nondecaying velocity and vorticity, II

Elaine Cozzi

Vol. 270 (2014), No. 2, 335–350

DOI: 10.2140/pjm.2014.270.335

Abstract

We consider solutions to the two-dimensional incompressible Navier–Stokes and Euler equations for which velocity and vorticity are bounded in the plane. We show that for every $T>0$, the Navier–Stokes velocity converges in $L^{\infty }\left(\left[0,T\right];L^{\infty }\left({ℝ}^2\right)\right)$ as viscosity approaches 0 to the Euler velocity generated from the same initial data. This improves our earlier results to the effect that the vanishing viscosity limit holds on a sufficiently short time interval, or for all time under the assumption of decay of the velocity vector field at infinity.

Keywords

fluid mechanics, inviscid limit

Mathematical Subject Classification 2010

Primary: 76D05

Milestones

Received: 8 May 2013

Revised: 31 October 2013

Accepted: 18 November 2013

Published: 22 August 2014