论文标题
均匀旋转涡流贴片的定量估计值
Quantitative estimates for uniformly-rotating vortex patches
论文作者
论文摘要
在本文中，我们得出了一些均匀旋转涡流贴片的定量估计值。我们证明，如果非radial简单连接的补丁$ d $是均匀旋转的，小角速度$ 0 <ω\ ll 1 $，那么补丁的最大点必须远离旋转的中心，至少具有$ω^{ - 1/2} $的距离。 For $m$-fold symmetric simply-connected rotating patches, we show that their angular velocity must be close to $\frac{1}{2}$ for $m\gg 1$ with the difference at most $O(1/m)$, and also obtain estimates on $L^{\infty}$ norm of the polar graph which parametrizes the boundary.
In this paper, we derive some quantitative estimates for uniformly-rotating vortex patches. We prove that if a non-radial simply-connected patch $D$ is uniformly-rotating with small angular velocity $0 < Ω\ll 1$, then the outmost point of the patch must be far from the center of rotation, with distance at least of order $Ω^{-1/2}$. For $m$-fold symmetric simply-connected rotating patches, we show that their angular velocity must be close to $\frac{1}{2}$ for $m\gg 1$ with the difference at most $O(1/m)$, and also obtain estimates on $L^{\infty}$ norm of the polar graph which parametrizes the boundary.
