American Institute of Mathematical Sciences

October  2016, 36(10): 5743-5761. doi: 10.3934/dcds.2016052

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

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

Received  October 2015 Revised  April 2016 Published  July 2016

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.
Citation: Yuji Sagawa, Hideaki Sunagawa. The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5743-5761. doi: 10.3934/dcds.2016052
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