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Journal Articles International Mathematics Research Notices Year : 2019

Smooth travelling-wave solutions to the inviscid surface quasigeostrophic equation

Didier Smets
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Abstract

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.

Dates and versions

hal-02980371 , version 1 (27-10-2020)

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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⟩
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