论文标题
不可压缩的$α$ - 消失磁盘外部的Euler方程
The incompressible $α$--Euler equations in the exterior of a vanishing disk
论文作者
论文摘要
在本文中，我们考虑了$α$ -Euler方程的外部固定磁盘的外部$ε$。我们假设最初的潜在涡度是紧凑的，并且独立于$ε$，并且在磁盘边界上未过滤速度的循环不取决于$ε$。我们证明，该问题的解决方案将$ε\至0 $收敛到整个平面中修改的$α$ - 欧拉方程的解决方案，在该平面上，位于磁盘中心的附加狄拉克在潜在的涡度中强加了。
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 $ε\to 0$, 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.
