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

Global well-posedness for a Modified 2D dissipative quasi-geostrophic equation with initial data in the critical Sobolev space $H^1$ - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: In this paper, we consider the following modified quasi-geostrophic equations$\partial t\theta +\Lambda^\alpha\theta +u\vec abla\theta =0$, $u=\Lambda^{\alpha-1}\mathcal{R}^\perp\theta$ where $\alpha \in 0,1$ is a fixedparameter. This equation was recently introduced by P. Constantin, G. Iyer andJ. Wu in \cite{CIW} as a modification of the classical quasi-geostrophicequation. In this paper, we prove that for any initial data $\theta \ast$ inthe Sobolev space $H^1\mathbb{R}^2,$ the equation MQG has a global andsmooth solution $\theta $ in $C\mathbb{R}^{+},H^1\mathbb{R}^2 .$

Author: ** Ramzi May**

Source: https://arxiv.org/