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

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

2003-07-22

arxiv.org/abs/math/0307295v1

SIAM J. Math. Analysis 36 (2005), 1130-1141

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In [1], T. Clopeau, A. Mikeli\'c, 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., Mikeli\'c, 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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