Optimal Gevrey Regularity for Supercritical Quasi-Geostrophic Equations

Abstract

We consider the two dimensional surface quasi-geostrophic equations with super-critical dissipation. For large initial data in critical Sobolev and Besov spaces, we prove optimal Gevrey regularity endowed with the same decay exponent as the linear part. This settles several open problems in Biswas (J Differ Equ 257(6):1753–1772, 2014), Biswas et al. (J Funct Anal 269(10):3083–3119, 2015).