On the V-states for the Generalized Quasi-Geostrophic Equations

Zineb Hassainia (1) , Taoufik Hmidi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha\in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the trivial solution at some explicit values of the angular velocity. This produces, inter alia, an infinite family of non stationary global solutions with uniqueness.

Mots clés: bifurcation theory; rotating patches; 2D inviscid SQG

Domaines: Equations aux dérivées partielles [math.AP]; Dynamique des Fluides [physics.flu-dyn]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Zineb Hassainia, Taoufik Hmidi. On the V-states for the Generalized Quasi-Geostrophic Equations. Communications in Mathematical Physics, 2015, 337 (1), pp.321-377. ⟨10.1007/s00220-015-2300-5⟩. ⟨hal-00991981⟩