Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions

Tsukasa Iwabuchi, Takayoshi Ogawa

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We consider the ill-posedness issue for the nonlinear Schrödinger equation with a quadratic nonlinearity. We refine the Bejenaru-Tao result by constructing an example in the following sense. There exist a sequence of time TN → 0 and solution uN(t) such that uN(TN)→∞ in the Besov space (σ > 2) for one space dimension. We also construct a similar ill-posed sequence of solutions in two space dimensions in the scaling critical Sobolev space H−1(ℝ2). We systematically utilize the modulation space for one dimension and the scaled modulation space for two dimensions.

Original languageEnglish
Pages (from-to)2613-2630
Number of pages18
JournalTransactions of the American Mathematical Society
Volume367
Issue number4
DOIs
Publication statusPublished - 2015 Apr 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Ill-posedness for the nonlinear Schrödinger equation with quadratic non-linearity in low dimensions'. Together they form a unique fingerprint.

Cite this