Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation

Abstract

We prove that linear instability implies non-linear instability in the energy norm for the critically dissipative quasi-geostrophic equation.

16 pages, corrected typos, a global bound that was obtained for the unforced equation by Kiselev-Nazarov-Volberg obtained for the forced equation and utilized in the paper;

References in corpus (3)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global Regularity for the Critical Dispersive Dissipative Surface Quasi-Geostrophic Equation
• Nonlinear instability for the Navier-Stokes equations

Cited by in corpus (12)

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• Absence of anomalous dissipation of energy in forced two dimensional fluid equations
• Uniformly attracting limit sets for the critically dissipative SQG equation
• Determining modes for the surface Quasi-Geostrophic equation
• The existence of a global attractor for the forced critical surface quasi-geostrophic equation in $L^2$
• Stability of Solutions to the Quasi-Geostrophic Equations in ${\mathbb{R}}^2$
• On nonlinear stabilization of linearly unstable maps
• On the forced surface quasi-geostrophic equation: Existence of steady states and sharp relaxation rates
• Nonlinear instability for the surface quasi-geostrophic equation in the supercritical regime