On the locally self-similar solution of the surface quasi-geostrophic equation with decaying or non-decaying profiles

摘要

Motivated by the numerical simulation and the study on several 1D models, we consider the locally self similar singular solutions for the surface quasi-geostrophic equation with decaying or non-decaying blowup profiles. Based on a suitable local L-p-inequality in terms of the profile and the bootstrapping method, we show some exclusion results and derive the asymptotic behavior of the possible blowup profiles. (C) 2016 Elsevier Inc. All rights reserved.