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1999 Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
Hideo Takaoka
Adv. Differential Equations 4(4): 561-580 (1999).

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.

Citation

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Hideo Takaoka. "Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity." Adv. Differential Equations 4 (4) 561 - 580, 1999.

Information

Published: 1999
First available in Project Euclid: 15 April 2013

zbMATH: 0951.35125
MathSciNet: MR1693278

Subjects:
Primary: 35Q55

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.4 • No. 4 • 1999
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