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

Abstract

We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schr{ö}dinger 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.

35 pages

References in corpus (2)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Asymptotic dynamic for dipolar Quantum Gases below the ground state energy threshold

Cited by in corpus (1)

• Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials