Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation

TL;DR

This paper establishes that in the critically dissipative quasi-geostrophic equation, linear instability necessarily leads to nonlinear instability when measured in the energy norm, highlighting a fundamental link between linear and nonlinear dynamics.

Contribution

It proves that linear instability implies nonlinear instability in the energy norm for the critically dissipative quasi-geostrophic equation, a significant theoretical result.

Findings

Linear instability implies nonlinear instability in the energy norm.

The result applies specifically to the critically dissipative quasi-geostrophic equation.

Provides a rigorous mathematical connection between linear and nonlinear instability.

Abstract

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