Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing

TL;DR

This paper proves global well-posedness and convergence of solutions for a supercritical quasi-geostrophic equation with large dispersive forcing, using Strichartz estimates, extending understanding of such equations in the supercritical regime.

Contribution

It establishes the global existence and strong convergence of solutions for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, a novel result in this context.

Findings

Global well-posedness for large initial data when dispersive forcing is large

Strong convergence of solutions as dispersive amplitude tends to infinity

Application of Strichartz estimates to supercritical quasi-geostrophic equations

Abstract

We consider the 2D quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation with large initial data. We also show the strong convergence result as the amplitude parameter goes to $\infty$. Both results rely on the Strichartz-type estimates for the corresponding linear equation.