speaker: Shuanglin Shao

time:  2025.5.22,9:30-10:30 pm

 place: Yifu Building 1417

 Abstract：

Motivated by the recent progress of the concentration-compactness approach in solving the     energy-critical and mass-critical dispersive equations such as nonlinear Schrodinger equations and the nonlinear wave equations, we investigated the extremizer problem for the Tomas-Stein inequality for the two dimensional sphere. We prove that extremizers exist and they are also smooth. We also prove that constant functions are local extremizers. The method is the concentration-compactness facilitated by a refined Bourgain-type Tomas-Stein inequality. This is a joint work with Michael Christ.