2020/10/14 by Jaemin Park, Park, Jaemin · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2010.06754
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≪ 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 (1)/(2) for m≫ 1 with the difference at most O(1/m), and also obtain estimates on L∞ norm of the polar graph which parametrizes the boundary.