On Solutions of Three Quasi-Geostrophic Models

TL;DR

This paper analyzes three quasi-geostrophic models, establishing global regularity results for regularized versions and extending Onsager's conjecture to these models, advancing understanding of weak solutions and turbulence.

Contribution

It introduces new regularization results for quasi-geostrophic models and extends Onsager's conjecture to these equations, linking turbulence theory with geophysical fluid dynamics.

Findings

Global regularity for regularized models with subcritical or critical indices

Extension of Onsager's conjecture to quasi-geostrophic equations

Development of dissipative solutions framework for these models

Abstract

We consider the 2D quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with subcritical or critical indices. The proof of Onsager's conjecture concerning weak solutions of the 3D Euler equations and the notion of dissipative solutions of Duchon and Robert are extended to weak solutions of the quasi-geostrophic equation.