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Strichartz refinements and bilinear restriction for Schrodinger operators

PDE and Applied Math Seminar

Speaker: Casey Jao, UC Berkeley
Location: 3106 MSB
Start time: Mon, May 7 2018, 3:10PM

We develop refined Strichartz estimates at $L^2$ regularityfor a class of Schr\"{o}dinger operators with time-dependent potentials, such the harmonic oscillator. Such refinements were first proved for the Euclidean Schr\{o}dinger equation (with zero potential) and play a

pivotal part in the global theory of mass-critical NLS. In the present nontranslation-invariant context the spacetime Fourier analytic techniques for the Euclidean equation do not work. We build on phase space techniques introduced in previous joint work with with

Killip and Visan, reduce to proving certain analogues of (adjoint) bilinear Fourier restriction estimates, and then adapt Tao's bilinear restriction estimate for paraboloids to more general Schr\"{o}dinger operators.