Joint Applied Math and Analysis Seminar on "On Global-in-Time Strichartz Estimates for the Semiperiodic Schrödinger Equation" by Alex Barron (Brown University)
Event Description:
Title: On Global-in-Time Strichartz Estimates for the Semiperiodic Schrödinger Equation
Abstract: We will discuss some recent results related to space-time
estimates for solutions to the linear Schrödinger equation on
manifolds which are products of tori and Euclidean space (e.g. a
cylinder embedded in R^3). On these manifolds it is possible to prove
certain analogues of the classical Euclidean Strichartz estimates
which are scale-invariant and global-in-time. These estimates -- which
are proved with harmonic analysis techniques -- are strong enough to
imply small-data scattering for solutions to the critical quintic NLS
on RxT and the critical cubic NLS on R^2xT (where T is the
one-dimensional torus).