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

DOI:
https://doi.org/10.1090/S0002-9939-04-07620-8

Published electronically:
July 12, 2004

MathSciNet review:
2084077

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-04-07620-8

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