Minimal mass blow-up solutions for the L2 critical NLS with inverse-square potential

Elek Csobo, Francois Genoud*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)

Abstract

We study minimal mass blow-up solutions of the focusing L2 critical nonlinear Schrödinger equation with inverse-square potential, i∂tu+Δu+[Formula presented]u+|u|[Formula presented]u=0,with N≥3 and 0<c<[Formula presented]. We first prove a sharp global well-posedness result: all H1 solutions with a mass (i.e. L2 norm) strictly below that of the ground states are global. Note that, unlike the equation in free space, we do not know if the ground state is unique in the presence of the inverse-square potential. Nevertheless, all ground states have the same, minimal, mass. We then construct and classify finite time blow-up solutions at the minimal mass threshold. Up to the symmetries of the equation, every such solution is a pseudo-conformal transformation of a ground state solution.

Original languageEnglish
Pages (from-to)110-129
Number of pages20
JournalNonlinear Analysis, Theory, Methods and Applications
Volume168
DOIs
Publication statusPublished - 2018

Keywords

  • Classification
  • Finite time blow-up
  • Inverse-square potential
  • L critical NLS
  • Sharp global well-posedness

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