Remarks on scattering for nonlinear Schrödinger equations

Kenji Nakanishi*, Tohru Ozawa

*この研究の対応する著者

研究成果: Article査読

58 被引用数 (Scopus)

抄録

We unify two distinct methods of the global analysis for the nonlinear Schrödinger equations, namely those in the Sobolev spaces and in the weighted spaces. Thus we can deal with various sums of power nonlinearies |u|p-1 u for 1 + 2/n < p < ∞, since the former works for p ≥ 1 + 4/N, while the latter for 1 + 2/n < p < 1 + 4/n. Even for a single power, our result is much simpler and slightly better than the previous ones as to restriction on the initial data. Moreover, we extend the result to the maximal regularity, thereby obtaining scattering at the lower critical value p = 1 + 8/ (√n2 + 4n + 36 + n + 2) for n ≥ 4. We also show the asymptotic completeness in FH1 without smallness for p ≥ l+8/( √ n2 + 12n + 4+n-2) and any n ∈ ℕ.

本文言語English
ページ(範囲)45-68
ページ数24
ジャーナルNonlinear Differential Equations and Applications
9
1
DOI
出版ステータスPublished - 2002 12月 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

フィンガープリント

「Remarks on scattering for nonlinear Schrödinger equations」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル