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

TL;DR

This paper extends the construction of smooth traveling-wave solutions from the inviscid surface quasi-geostrophic equation to a broader class involving general fractional Laplacians, enhancing understanding of these solutions.

Contribution

It generalizes previous solutions to include any fractional Laplacian, broadening the scope of smooth traveling-wave solutions in quasi-geostrophic equations.

Findings

Constructed solutions for a wider class of fractional Laplacians.

Extended the existence of smooth traveling-wave solutions.

Provided a framework for analyzing solutions with different fractional orders.

Abstract

In a recent article by Gravejat and Smets, 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 solution to a more general class of quasi-geostrophic equation where the half-laplacian is replaced by any fractional laplacian.