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arXiv · 2203.14690

The incompressible $\alpha$--Euler equations in the exterior of a vanishing disk

Adriana Valentina Busuioc·Dragos Iftimie·Milton Lopes Filho·Helena Nussenzveig Lopes
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Abstract

In this article we consider the $\alpha$--Euler equations in the exterior of a small fixed disk of radius $\epsilon$. We assume that the initial potential vorticity is compactly supported and independent of $\epsilon$, and that the circulation of the unfiltered velocity on the boundary of the disk does not depend on $\epsilon$. We prove that the solution of this problem converges, as $\epsilon \to 0$, to the solution of a modified $\alpha$--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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Adriana Valentina Busuioc, Dragos Iftimie, Milton Lopes Filho, Helena Nussenzveig Lopes. 2022-03-28. The incompressible $\alpha$--Euler equations in the exterior of a vanishing disk. https://arxiv.org/abs/2203.14690

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