The incompressible α--Euler equations in the exterior of a vanishing disk

2022/03/28 by Busuioc, Adriana Valentina, Iftimie, Dragos, Filho, Milton Lopes +1
#35Q35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.14690

Abstract

In this article we consider the α--Euler equations in the exterior of a small fixed disk of radius ε. We assume that the initial potential vorticity is compactly supported and independent of ε, and that the circulation of the unfiltered velocity on the boundary of the disk does not depend on ε. We prove that the solution of this problem converges, as ε→ 0, to the solution of a modified α--Euler equation in the full plane where an additional Dirac located at the center of the disk is imposed in the potential vorticity.

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