Tuesday Seminar of Analysis

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Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2012/05/15

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
MIZUTANI, Haruya (Research Institute for Mathematical Sciences, Kyoto University)
Strichartz estimates for Schr\\"odinger equations with variable coefficients and unbounded electromagnetic potentials (JAPANESE)
[ Abstract ]
In this talk we consider the Cauchy problem for Schr\\"odinger equations with variable coefficients and unbounded potentials. Under the assumption that the Hamiltonian is a long-range perturbation of the free Schr\\"odinger operator, we construct an outgoing parametrix for the propagator near infinity, and give applications to sharp Strichartz estimates. The basic idea is to combine the standard approximation by using a time dependent modifier, which is not in the semiclassical regime, with the semiclassical approximation of Isozaki-Kitada type. We also show near sharp Strichartz estimates without asymptotic conditions by using local smoothing effects.