Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential

Alex H. Ardila; Masaru Hamano; Masahiro Ikeda

paper

Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential

arXiv:2202.11640

Abstract

In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when $E_{V} (u_{0}) M (u_{0}) = E_{0} (Q) M (Q)$ . Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold.

21 pages