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2003 Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament
J. Segata
Differential Integral Equations 16(7): 841-864 (2003).

Abstract

We consider the time-local well-posedness for the initial-value problem of the fourth-order nonlinear Schrödinger-type equation in one space dimension which describes the motion of the vortex filament. By using the method of Fourier restriction norm introduced by Bourgain [3] and Kenig-Ponce-Vega [17]--[19], we show the time-local well-posedness in the Sobolev space $H^s(\mathbb R)$ with $s\ge1/2$ under certain coefficient conditions.

Citation

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J. Segata. "Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament." Differential Integral Equations 16 (7) 841 - 864, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1042.35077
MathSciNet: MR1988728

Subjects:
Primary: 35Q55
Secondary: 35B30, 76D17

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 7 • 2003
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