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The lifespan of small solutions to cubic derivative nonlinear Schr\"odinger equations in one space dimension

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arxiv 1511.03126 v1 pith:RU7BMN25 submitted 2015-11-10 math.AP

classification math.AP
keywords nonlinearcubicderivativedimensionequationsinitiallifespanodinger
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Consider the initial value problem for cubic derivative nonlinear Schr\"odinger 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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