The Surface Quasigeostrophic equation on the sphere

Analysis Seminar
Topic:The Surface Quasigeostrophic equation on the sphere
Speaker:Angel Martinez Martinez
Affiliation:Member, School of Mathematics
Date:Monday, October 28
Time/Room:5:00pm - 6:00pm/Simonyi Hall 101
Video Link: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.