Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations

TL;DR

This paper demonstrates the existence of nontrivial steady-state weak solutions to the surface quasi-geostrophic equations on a 2D periodic domain, highlighting non-uniqueness issues in these equations.

Contribution

It provides the first construction of nontrivial stationary weak solutions, revealing non-uniqueness in the solutions to the surface quasi-geostrophic equations.

Findings

Existence of nontrivial stationary weak solutions.

Non-uniqueness of solutions established.

Solutions constructed on the 2D periodic torus.

Abstract

We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.