A sharp global-in-time Strichartz estimate for the Schrodinger equation on the infinite 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 in interesting cases (meaning the initial data needs to be in a Sobolev space rather than L^2). On non-compact manifolds it is a challenging problem to understand when one can have good space-time estimates with no loss of derivatives.

In this talk we discuss an endpoint Strichartz-type estimate for the linear Schrodinger equation on the infinite cylinder (or, equivalently, with one periodic component and one Euclidean component). Our estimate is sharp, scale-invariant, and requires only L^2 data. This contrasts the purely periodic case where some loss of derivatives is necessary at the endpoint, as originally observed by Bourgain.

Joint work with M. Christ and B. Pausader.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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