AN ANALYTICAL AND NUMERICAL STUDY OF STEADY PATCHES IN THE DISC

Francisco de La Hoz (1) , Zineb Hassainia (2) , Taoufik Hmidi (3) , Joan Mateu (4)

1 UPV / EHU - University of the Basque Country = Euskal Herriko Unibertsitatea
2 NYU - New York University [New York]
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 UAB - Departament de Matemàtiques [Barcelona]

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.

Mots clés: Euler equations; V-states; bifurcation

Domaines: Equations aux dérivées partielles [math.AP]

Francisco de La Hoz, Zineb Hassainia, Taoufik Hmidi, Joan Mateu. AN ANALYTICAL AND NUMERICAL STUDY OF STEADY PATCHES IN THE DISC. Analysis & PDE, 2016, 9 (7), pp.1609-1670. ⟨10.2140/apde.2016.9.1609⟩. ⟨hal-01365289⟩