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ID 52598
ファイル
言語
英語
著者
内容記述(抄録等)
We study the nonlinear Schrödinger equation (NLS)
∂tu+iΔu=iλ|u|p−1u
in R1+n, where n≥3, p>1, and λ∈C. We prove that (NLS) is locally well-posed in Hs if 1<s<min{4;n/2} and max{1;s/2}<p<1+4/(n−2s). To obtain a good lower bound for p, we use fractional order Besov spaces for the time variable. The use of such spaces together with time cut-off makes it difficult to derive positive powers of time length from nonlinear estimates, so that it is difficult to apply the contraction mapping principle. For the proof we improve Pecher's inequality (1997), which is a modification of the Strichartz estimate, and apply this inequality to the nonlinear problem together with paraproduct formula.
主題
Nonlinear Schrödinger equations
well-posedness
Besov spaces
掲載誌名
Communications on Pure & Applied Analysis
18
3
開始ページ
1359
終了ページ
1374
ISSN
1534-0392
ISSN(Online)
1553-5258
発行日
2019
DOI
出版者
American Institute of Mathematical Sciences
資料タイプ
学術雑誌論文
ファイル形式
PDF
著者版/出版社版
出版社版
部局
総合理工学部