# Analysis Seminar

**Topic: **The Surface Quasigeostrophic equation on the sphere

**Speaker: **Angel Martinez Martinez

**Affiliation: **Member, School of Mathematics

**Date & Time: **Monday October 28th, 2019, 5:00pm - 6:00pm

**Location: **Simonyi Hall 101

**Video:** https://video.ias.edu/analysis/2019/1028-AngelMartinezMartinez

In this talk I will describe joint work with D. Alonso-Orán and A. Córdoba where we extend a result, proved independently by Kiselev-Nazarov-Volberg and Caffarelli-Vasseur, for the critical dissipative SQG equation on a two dimensional sphere. The proof relies on De Giorgi technique following Caffarelli-Vasseur intermingled with a nonlinear maximum principle that appeared later in the approach of Constantin-Vicol. The final result can be paraphrased as follows: if the data is sufficiently smooth initially then it is smooth for all times.