Global existence, scattering and blow-up for the focusing NLS on the hyperbolic space

DOI10.4310/DPDE.2015.v12.n1.a4zbMath1316.35259arXiv1411.0846MaRDI QIDQ2346011

Thomas Duyckaerts, Valeria Banica

Publication date: 29 May 2015

Published in: Dynamics of Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0846

zbMATH Keywords

scatteringnonlinear Schrödinger equationblow-uphyperbolic space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Blow-up in context of PDEs (35B44) PDEs on manifolds (35R01)

Related Items (8)

Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\) ⋮ Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation ⋮ Uniqueness of the ground state of the NLS on \(\mathbb{H}^d\) via analytical and topological methods ⋮ On the high–low method for NLS on the hyperbolic space ⋮ Qualitative properties of stationary solutions of the NLS on the hyperbolic space without and with external potentials ⋮ Existence and Stability of Schrödinger Solitons on Noncompact Manifolds ⋮ Global existence and finite time blow-up for a parabolic system on hyperbolic space ⋮ Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\)

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