An analytical and numerical study of steady patches in the disc

Abstract

In this paper, we prove the existence of $m$-fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the lowest symmetries $m=1$ and $m=2$. We also discuss some numerical experiments highlighting the interaction between the boundary of the patch and the rigid one.

56 pages

References in corpus (2)

• Doubly connected V-states for the planar Euler equations
• Uniformly rotating analytic global patch solutions for active scalars