The initial value problem for the 1-D semilinear Schrodinger equation in Besov spaces

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We define a class of Besov type spaces which is a generalization of that defined by Kenig-Ponce-Vega ([{4}], [{5}]) in their study on KdV equation and non-linear Schrödinger equation. Using these spaces, we prove the following results. the 1-dimendional semilinear Schrödinger equation with the nonlinear term c<SUB>1</SUB>u<SUP>2</SUP>+c<SUB>2</SUB>overline{u}<SUP>2</SUP> has a unique local-in-time solution for the initial data∈ B<SUB>2, 1</SUB><SUP>-3/4</SUP>, and that with cuoverline{u} has a unique local-in-time solution for the initial data∈ B<SUB>2, 1</SUB>^{-1/4, \#}. Note that B<SUB>2, 1</SUB>^{-1/4, \#}(\bm{R})⊃ B_{2\bm{, }1}<SUP>-1/4</SUP>(\bm{R})⊃ H<SUP>s</SUP>(\bm{R}) for any s>-1/4.

収録刊行物

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 56(3), 853-888, 2004-07-01

    一般社団法人 日本数学会

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各種コード

  • NII論文ID(NAID)
    10013359007
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    7015212
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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