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

Abstract

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

arXiv comment8 pages, improved regularity and added references

References in corpus (3)

• Dissipative continuous Euler flows
• Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions
• A direct approach to nonuniqueness and failure of compactness for the SQG equation

Cited by in corpus (3)

• Strong illposedness for SQG in critical Sobolev spaces
• Optimal Gevrey regularity for supercritical quasi-geostrophic equations
• The importance of Luis Caffarelli's work in the study of fluids