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Dispersive Estimates for the Schr枚dinger Flow inside General Convex Domains and Applications to the Cubic NLS in 3D

Analysis Seminar

Dispersive Estimates for the Schr枚dinger Flow inside General Convex Domains and Applications to the Cubic NLS in 3D

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Fabrice Planchon, Sorbonne Universit茅 and Institut Universitaire de France

We obtain fixed time decay rate for the linear (semi-classical) Schr枚dinger flow inside a general strictly convex domain.听
Corresponding Strichartz estimates allow to solve the cubic NLS in the natural energy class on such 3D convex domains. This is joint work with O. Ivanovici. We will start by reviewing earlier work (with O. Ivanovici, R. Lascar and G. Lebeau) on the wave equation on such domains, as the optimal decay rates in all regimes for waves turn out to be crucial to deal with Schr枚dinger.

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