Smooth travelling-wave solutions to the inviscid surface quasigeostrophic equation

Philippe Gravejat (1) , Didier Smets (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 LJLL (UMR_7598) - 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.

Domains: Mathematics [math]

Philippe Gravejat, Didier Smets. Smooth travelling-wave solutions to the inviscid surface quasigeostrophic equation. International Mathematics Research Notices, 2019, 2019 (6), pp.1744-1757. ⟨10.1093/imrn/rnx177⟩. ⟨hal-02980371⟩