Ill-posedness for a system of quadratic nonlinear Schrödinger equations in two dimensions

Tsukasa Iwabuchi, Takayoshi Ogawa, Kota Uriya

Research output: Contribution to journalArticlepeer-review

Abstract

This paper concerns the ill-posedness issue for a system of quadratic nonlinear Schrödinger equations in two dimensions. From previous studies for the large time behavior of the solution to the system, one may expect that the critical regularity to show the well-posedness depends on the dispersion coefficients. To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for the mass resonance case and show the norm inflation for other cases.

Original languageEnglish
Pages (from-to)136-163
Number of pages28
JournalJournal of Functional Analysis
Volume271
Issue number1
DOIs
Publication statusPublished - 2016 Jul 1

Keywords

  • Ill-posedness
  • Mass resonance
  • Norm inflation
  • System of nonlinear Schrödinger equations

ASJC Scopus subject areas

  • Analysis

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