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ON GLOBAL ROUGH SOLUTIONS TO A NON-LINEAR SCHRÖDINGER SYSTEM

Published online by Cambridge University Press:  01 September 2009

LI MA ,
XIANFA SONG  and
LIN ZHAO
LI MA
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Peking 100084, P.R. China e-mail: lma@math.tsinghua.edu.cn
XIANFA SONG
Affiliation:
Department of Mathematics, Tianjin University, Tianjin 300072, P.R. China e-mail: songxianfa2004@163.com
LIN ZHAO
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing, P.R. China e-mail: zhaolin05@mails.tsinghua.edu.cn
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Abstract

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The non-linear Schrödinger systems arise from many important physical branches. In this paper, employing the ‘I-method’, we prove the global-in-time well-posedness for a coupled non-linear Schrödinger system in Hs(n) when n = 2, s > 4/7 and n = 3, s > 5/6, respectively, which extends the results of J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao (Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, Math Res. Lett. 9, 2002, 659–682) to the system.

Keywords

Primary 35Q55
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 499 - 511
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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