Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation

Philippe Gravejat (1) , Didier Smets (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 LJLL - Laboratoire Jacques-Louis Lions

We construct families of smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation (SQG). These solutions can be viewed as the equivalents for this equation of the vortex anti-vortex pairs in the context of the incompressible Euler equation. Our argument relies on the stream function formulation and eventually amounts to solving a fractional nonlinear elliptic equation by variational methods.

Mots clés: Surface quasi-geostrophic equation; Travelling waves

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Philippe Gravejat, Didier Smets. Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation. 2017. ⟨hal-01525558⟩