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Article Dans Une Revue Communications in Mathematical Sciences Année : 2021

Global dynamics below the ground states for NLS under partial harmonic confinement

Résumé

We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schrödinger equation under partial harmonic confinement. We establish a necessary and sufficient condition on the initial data below the ground states to determine the global behavior (blow-up/scattering) of the solution. Our proof of scattering is based on the varia-tional characterization of the ground states, localized virial estimates, linear profile decomposition and nonlinear profiles.
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Dates et versions

hal-02864076 , version 1 (10-06-2020)

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Alex H Ardila, Rémi Carles. Global dynamics below the ground states for NLS under partial harmonic confinement. Communications in Mathematical Sciences, 2021, 19 (4), pp.993-1032. ⟨10.4310/CMS.2021.v19.n4.a6⟩. ⟨hal-02864076⟩
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