Quintic NLS in the exterior of a strictly convex obstacle
By Rowan Killip, Monica Visan, Xiaoyi Zhang. 2012
68 citations recorded by the source corpus.
We consider the defocusing energy-critical nonlinear Schr\"odinger equation in the exterior of a smooth compact strictly convex obstacle in three dimensions. For the initial-value problem with Dirichlet boundary condition we prove global well-posedness and scattering for all initial data in the energy space.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1c7b9c0935e70c848a6b69016e31dc64caf3a377
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In Mathematical Physics
- Jerry L. Bona
- Bingyu Zhang
- Nikolay Tzvetkov
- Nicola Visciglia
- Benoit Pausader
- Zaher Hani
- Shu-Ming Sun
- Andrei V. Faminskii
Citations in the corpus
- Nonhomogeneous Boundary-Value Problems for One-Dimensional Nonlinear Schr\"odinger Equations (2015, background): “ndary conditions has not progressed to the same extent (see [30, 19, 20, 21, 22, 23, 45, 46, 52, 68, 69, 70, 71] and more recent work on the boundary-value problems of some other dispersive equations [55], and the references therein). In this paper, the goal is to advance the study of the IBVP’s (1.”
- MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS (2013, background): “jujp 1u; p>1 (1.2) dates back at least to [21]. The rst natural question is the issue of global existence of solutions, and many works have investigated this problem in dierent geometric settings [4, 5, 6, 14, 19, 23, 24, 25, 30, 37, 50, 52, 57, 58, 59, 60, 61, 62, 69, 71, 72, 77, 84, 89]. The co”