Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction

Van Duong Dinh, Luigi Forcella

Research output: Contribution to journalArticlepeer-review

Abstract

We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.

Original languageEnglish
Article number178
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume72
Issue number5
Early online date4 Sep 2021
DOIs
Publication statusE-pub ahead of print - 4 Sep 2021

Keywords

  • Blow-up
  • Grow-up
  • Nonlinear Schrödinger systems
  • Quadratic-type interactions

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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