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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remark on well-posedness for the fourth order nonlinear Schrödinger type equation


Author: Jun-ichi Segata
Journal: Proc. Amer. Math. Soc. 132 (2004), 3559-3568
MSC (2000): Primary 35Q55
Published electronically: July 12, 2004
MathSciNet review: 2084077
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Abstract: We consider the initial value problem for the fourth order nonlinear Schrödinger type equation (4NLS) related to the theory of vortex filament. In this paper we prove the time local well-posedness for (4NLS) in the Sobolev space, which is an improvement of our previous paper.


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Additional Information

Jun-ichi Segata
Affiliation: Graduate School of Mathematics, Kyushu University, 10-1, Hakozaki 6-chôme, Higashi-ku, Fukuoka 812-8581, Japan
Email: segata@math.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07620-8
PII: S 0002-9939(04)07620-8
Keywords: Fourth order nonlinear Schr\"odinger type equation, local well-posedness
Received by editor(s): April 30, 2003
Published electronically: July 12, 2004
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2004 American Mathematical Society