Global well-posedness for a Modified 2D dissipative quasi-geostrophic equation with initial data in the critical Sobolev space $H^1$

Ramzi May

In this paper, we consider the following modified quasi-geostrophic equations ${\partial }_t\theta +{\Lambda }^{\alpha }\theta +u\vec{\nabla }\theta =0$, $u={\Lambda }^{\alpha -1}{\mathcal{R}}^{\perp }(\theta )$ where $\alpha \in ]0,1[$ is a fixed param…