On the cubic NLS on 3D compact domains

Abstract

We prove bilinear estimates for the Schrödinger equation on 3D domains, with Dirichlet boundary conditions. On non-trapping domains, they match the ${\mathbb{R}}^3$ case, while on bounded domains they match the generic boundary less manifold case. As an application, we obtain global well-posedness for the defocusing cubic NLS for data in $H_0^s(\Omega )$, $1<s\le 3$, with $\Omega$ any bounded domain with smooth boundary.

15 pages, updated references and corrected typos. To appear in Journal of the Institute of Mathematics of Jussieu

References in corpus (4)

• On the energy critical Schrodinger equation in 3D non-trapping domains
• Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d=4$
• Global regularity of critical Schrödinger maps: subthreshold dispersed energy
• Global regularity for the energy-critical NLS on ${\mathbb{S}}^3$

Cited by in corpus (2)

• Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
• Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space