The lifespan of small solutions to cubic derivative  nonlinear Schrödinger equations in one space dimension

Yuji  Sagawa; Hideaki  Sunagawa

doi:10.3934/dcds.2016052

Article Contents

2016, Volume 36, Issue 10: 5743-5761. Doi: 10.3934/dcds.2016052

This issue Previous Article Solitary waves for an internal wave model Next Article Sharp global well-posedness of the BBM equation in $L^p$ type Sobolev spaces

The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension

Yuji Sagawa^1, and
Hideaki Sunagawa^1,

1.
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043

Received: September 30, 2015

Revised: March 31, 2016

Published: May 2017

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Abstract

Consider the initial value problem for cubic derivative nonlinear Schrödinger equations in one space dimension. We provide a detailed lower bound estimate for the lifespan of the solution, which can be computed explicitly from the initial data and the nonlinear term. This is an extension and a refinement of the previous work by one of the authors [H. Sunagawa: Osaka J. Math. 43 (2006), 771--789], in which the gauge-invariant nonlinearity was treated.

Keywords:

Derivative nonlinear Schrödinger equations,
lifespan,
detailed lower bound.

Mathematics Subject Classification: 35Q55, 35B40.

Citation:

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