<p>题目：Variation on a theme of Caffarelli and Vasseur</p>



<p>报告时间：5月25日下午: 2:00--5:00 (星期三)</p>



<p>报告时间：5月27日下午: 2:00--5:00 (星期五)</p>



<p>报告时间：6月2日下午:  2:00--5:00 (星期三)</p>



<p>报告人：　中科院数学所   郝成春（副研究员）</p>



<p>论文摘要：Recently, using De Giorgi-type techniques, Caffarelli and Vasseur have shown that a certain class of weak solutions to the drift diffusion equation with initial data in $L^2$ gain Hölder continuity, provided that the BMO norm of the drift velocity is bounded uniformly in time. We show a related result: a uniform bound on the BMO norm of a smooth velocity implies a uniform bound on the $C^eta$ norm of the solution for some $eta > 0$. We apply elementary tools involving the control of Hölder norms by using test functions. In particular, our approach offers a third proof of the global regularity for the critical surface quasigeostrophic (SQG) equation in addition to the two proofs obtained earlier.</p>