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2021•Comptes Rendus MathématiqueOpen access

Smooth traveling-wave solutions to the inviscid surface quasi-geostrophic equations

Ludovic Godard-Cadillac

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Abstract

In a recent article by Gravejat and Smets [7], it is built smooth solutions to the inviscid surface quasi-geostrophic equation that have the form of a traveling wave. In this article we work back on their construction to provide similar solutions to a more general class of quasi-geostrophic equation where the half-laplacian is replaced by any fractional laplacian.

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What this paper is about

In a recent article by Gravejat and Smets [7], it is built smooth solutions to the inviscid surface quasi-geostrophic equation that have the form of a traveling wave. In this article we work back on their construction to provide similar solutions to a more general class of quasi-geostrophic equation where the half-laplacian is replaced by any fractional laplacian.

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Available abstract

In a recent article by Gravejat and Smets [7], it is built smooth solutions to the inviscid surface quasi-geostrophic equation that have the form of a traveling wave. In this article we work back on their construction to provide similar solutions to a more general class of quasi-geostrophic equation where the half-laplacian is replaced by any fractional laplacian.

Key concepts: Inviscid flow, Geostrophic wind, Mathematics, Mathematical analysis, Surface (topology), Class (philosophy), Fractional Laplacian, Laplace operator

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