#### Vol. 9, No. 7, 2016

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An analytical and numerical study of steady patches in the disc

### Francisco de la Hoz, Zineb Hassainia, Taoufik Hmidi and Joan Mateu

Vol. 9 (2016), No. 7, 1609–1670
DOI: 10.2140/apde.2016.9.1609
##### Abstract

We prove the existence of $m$-fold rotating patches for the Euler equations in the disc, for the 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.

##### Keywords
Euler equations, $V$-states, bifurcation
##### Mathematical Subject Classification 2010
Primary: 35Q35, 37G40, 35Q31
Secondary: 76B47