Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential

Dinh Van Duong

Mathematische Nachrichten, 2021, vol. 294, issue 4, 672-716

Abstract: We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the ground state for the equation with radially symmetric initial data. We then establish blow‐up criteria for non‐radial solutions to the equation. In the defocusing case, we also prove the energy scattering for the equation with radially symmetric initial data.

Date: 2021
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