ncku-talk2016-06-02

Colloquium

DATE 2016-06-02　16:10-17:00

PLACE 數學館3174教室

SPEAKER Shuanglin Shao 教授（堪薩斯大學數學系）

TITLE On Characterization of the Strichartz Inequality for the Schrodinger Equations

ABSTRACT The Strichartz inequality is a fundamental estimate in dispersive partial differential equations. Recently the extremal problem for this type of inequalities attracts a lot of attention starting with the work of M. Kunze for the one dimension Strichartz inequality for the Schrodinger equation. Foschi and Hundertmark-Zharnitsky independently proved that Gaussian functions are extremizers for the Strichartz inequality when the spatial dimension is one or two, and completely characterize the extremizers. In this talk, we will briefly review the background of this problem. Then based on the functional inequality of Foschi, we give an alternative proof that Gaussians are extremizers. The large part of the argument is to prove that the critical points to the Euler-Lagrange equation is complex analytic on $C^2$. This is a joint work with Jin-Cheng Jiang.

Colloquium

DATE	2016-06-02　16:10-17:00

PLACE	數學館3174教室

SPEAKER	Shuanglin Shao 教授（堪薩斯大學數學系）

TITLE	On Characterization of the Strichartz Inequality for the Schrodinger Equations

ABSTRACT	The Strichartz inequality is a fundamental estimate in dispersive partial differential equations. Recently the extremal problem for this type of inequalities attracts a lot of attention starting with the work of M. Kunze for the one dimension Strichartz inequality for the Schrodinger equation. Foschi and Hundertmark-Zharnitsky independently proved that Gaussian functions are extremizers for the Strichartz inequality when the spatial dimension is one or two, and completely characterize the extremizers. In this talk, we will briefly review the background of this problem. Then based on the functional inequality of Foschi, we give an alternative proof that Gaussians are extremizers. The large part of the argument is to prove that the critical points to the Euler-Lagrange equation is complex analytic on $C^2$. This is a joint work with Jin-Cheng Jiang.