On the inviscid limit for 2D incompressible flow with Navier friction condition

2003/07/22 by M. C. Lopes Filho, H. J. Nussenzveig Lopes, G. V. Planas
Mathematics · #math.AP #msc:35Q30 #msc:76D10 #msc:76D30 #msc:76B03

paper · pdf

published as SIAM J. Math. Analysis 36 (2005), 1130-1141 · 18 pages

arxiv created 2003/07/22 · arxiv updated 2009/12/01

Abstract

In [1], T. Clopeau, A. Mikelić, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit satisfies the incompressible Euler equations and their result ultimately includes flows generated by bounded initial vorticities. Our purpose in this article is to adapt and, to some extent, simplify their argument in order to include p-th power integrable initial vorticities, with p>2. [1] Clopeau, T., Mikelić, A., Robert, R., \it On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions, Nonlinearity \bf 11 (1998) 1625--1636.

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