In this paper, we study the critical dissipative quasi-geostrophic equations in scaling invariant spaces. We prove that there exists a global-in-time small solution for small initial data ??0???L?????? H1 such that (??0)???L???, where is the Riesz transform. As a corollary, we prove that if in addition, ??0???B???,q0, 1???q<2, is small enough, then ?????Lt???B???,q0???Lt1B???,q1. ?? 2010 Elsevier Ltd. All rights reserved.
Bae, H. (2011). Global well-posedness for the critical dissipative quasi-geostrophic equations in L??? Nonlinear Analysis, Theory, Methods and Applications, 74(5), 1995–2002. https://doi.org/10.1016/j.na.2010.11.006