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arXiv · 1210.4362

On the cubic NLS on 3D compact domains

Fabrice Planchon
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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 $H^s_0(Ω)$, $1<s\leq 3$, with $Ω$ any bounded domain with smooth boundary.

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Fabrice Planchon. 2013-01-04. On the cubic NLS on 3D compact domains. https://doi.org/10.1017/s1474748013000017

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