Global Regularity for the Critical Dispersive Dissipative Surface Quasi-Geostrophic Equation

TL;DR

This paper proves the global existence of smooth solutions for a critical dispersive dissipative surface quasi-geostrophic equation using a maximum principle and moduli of continuity, advancing understanding of its long-term behavior.

Contribution

It establishes the global regularity for the critical dispersive dissipative surface quasi-geostrophic equation, a novel result in the field.

Findings

Global existence of smooth solutions is proven.

Maximum principle involving moduli of continuity is used.

Results apply to sufficiently smooth initial data.

Abstract

We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done using a maximum principle for the solutions involving conservation of a certain family of moduli of continuity.