Differential and Integral Equations

Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament

J. Segata

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.

Article information

Source
Differential Integral Equations, Volume 16, Number 7 (2003), 841-864.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060600

Mathematical Reviews number (MathSciNet)
MR1988728

Zentralblatt MATH identifier
1042.35077

Citation

Segata, J. Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament. Differential Integral Equations 16 (2003), no. 7, 841--864. https://projecteuclid.org/euclid.die/1356060600