A sharp global Strichartz estimate for the Schrodinger equation on the cylinder

Abstract: The classical Strichartz estimates show that a solution to the linear Schrodinger equation on Euclidean space is in certain Lebesgue spaces globally in time provided the initial data is in $L^2$. On compact manifolds one can no longer have global control, and some loss of derivatives is necessary (meaning the initial data needs to be in a Sobolev space rather than $L^2$). In 'intermediate' cases it is a challenging question to understand when one can have good space-time estimates with no loss of derivatives.

In this talk we discuss a global-in-time Strichartz-type estimate for the linear Schrodinger equation on the cylinder. Our estimate is sharp, scale-invariant, and requires only $L^2$ data. Joint work with M. Christ and B. Pausader.

analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.