A direct approach to nonuniqueness and failure of compactness for the SQG equation

Abstract

We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [Buckmaster-Shkoller-Vicol, '16]. Our approach proceeds directly at the level of the scalar field. Furthermore, we prove that every smooth scalar field with compact support that conserves the integral can be realized as a weak limit of solutions to SQG.

References in corpus (5)

• Dissipative continuous Euler flows
• Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations
• Lack of uniqueness for weak solutions of the incompressible porous media equation
• Energy Spectrum of Quasi-Geostrophic Turbulence
• h-Principles for the incompressible Euler equations

Cited by in corpus (5)

• Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations
• Global Solutions of a Surface Quasi-Geostrophic Front Equation
• Strong illposedness for SQG in critical Sobolev spaces
• Onsager's Conjecture for Subgrid Scale $\alpha$-Models of Turbulence
• Probabilistic Approaches to The Energy Equality in Forced Surface Quasi-Geostrophic Equations