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

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概要

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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.

• 社団法人 日本数学会の論文
• 2004-07-01

著者

• Taoka Shifu

  Department Of Mathematics Chuo University

• MURAMATU Tosinobu

  Department of Mathematics Chuo University

関連論文

• The initial value problem for the 1-D semilinear Schrodinger equation in Besov spaces
• L p and Besov maximal estimates for solutions to the Schrodinger equation
• On the Dual of Besov Spaces

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