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Home » Research Seminar: The Focusing Cubic NLS on Exterior Domains in Three Dimensions

Seminar

Research Seminar: The Focusing Cubic NLS on Exterior Domains in Three Dimensions September 30, 2015 (11:30 AM PDT - 12:30 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Xiaoyi Zhang (University of Iowa)
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We consider the focusing cubic NLS in the exterior Ω of a smooth, compact, strictly convex obstacle in three dimensions. We prove that the threshold for global existence and scattering is the same as for the prob- lem posed on Euclidean space. Specifically, we prove that if E(u0)M(u0) < E(Q)M(Q) and ∥∇u0∥2∥u0∥2 <∥∇Q∥2∥Q∥2, the corresponding solution to the initial-value problem with Dirichlet boundary conditions exists globally and scatters to linear evolutions asymptotically in the future and in the past. Here,Q(x) denotes the ground state for the focusing cubic NLS in R3.

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