The Surface Quasigeostrophic equation on the sphere

The Surface Quasigeostrophic equation on the sphere -Angel Martinez Martinez

Angel Martinez Martinez
Member, School of Mathematics
October 28, 2019

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.

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