Global large, smooth solutions of the 2D surface quasi-geostrophic equations

TL;DR

This paper proves the global regularity of smooth solutions to the 2D surface quasi-geostrophic equations with super-critical dissipation for large initial data, advancing understanding of these equations without smallness constraints.

Contribution

It establishes global regularity results for large initial data in 2D SQG equations without requiring smallness in the initial data norms.

Findings

Global smooth solutions exist for large initial data

No smallness condition on initial data in $L^ abla( ext{R}^2)$ and $H^3( ext{R}^2)$

Improves previous results by Liu-Pan-Wu

Abstract

In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with super-critical dissipation for a class of large initial data, where the velocity and temperature can be arbitrarily large in spaces $L^\infty(\mathbb{R}^2)$ and $H^3(\mathbb{R}^2)$. This result could be seen as an improvement work of Liu-Pan-Wu \cite{Liu}, for it's without any smallness hypothesis of the $L^\infty(\mathbb{R}^2)$ norm of the initial data.