Advances in Differential Equations

Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity

Hideo Takaoka

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Abstract

We show the well-posedness in $H^{\frac 12 }$ of the Cauchy problem for a certain class of one dimensional nonlinear Schrödinger equations with the derivative nonlinearity. This is an improvement of results in $H^1$ by N. Hayashi and T. Ozawa [2,3,4,20]. Our results can cover the derivative nonlinear Schrödinger equation. Our proof is based on the Fourier restriction norm method and the gauge transformation.

Article information

Source
Adv. Differential Equations Volume 4, Number 4 (1999), 561-580.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366031032

Mathematical Reviews number (MathSciNet)
MR1693278

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Takaoka, Hideo. Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity. Adv. Differential Equations 4 (1999), no. 4, 561--580. https://projecteuclid.org/euclid.ade/1366031032.


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