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arXiv · 1511.03126

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

Yuji Sagawa·Hideaki Sunagawa
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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 where the gauge-invariant nonlinearity was treated.

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Yuji Sagawa, Hideaki Sunagawa. 2015-11-10. The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension. https://doi.org/10.3934/dcds.2016052

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