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

Yuji Sagawa, Hideaki Sunagawa

Type: Article

Publication Date: 2016-07-01

Citations: 8

DOI: https://doi.org/10.3934/dcds.2016052

Abstract

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

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