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

Tsukasa Iwabuchi, Takayoshi Ogawa

研究成果: Article査読

18 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2613-2630
ページ数18
ジャーナルTransactions of the American Mathematical Society
367
4
DOI
出版ステータスPublished - 2015 4 1

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

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