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arXiv · 1605.03247

Almost global existence for cubic nonlinear Schr\"odinger equations in one space dimension

Jason Murphy·Fabio Pusateri
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Abstract

We consider non-gauge-invariant cubic nonlinear Schr\"odinger equations in one space dimension. We show that initial data of size $\varepsilon$ in a weighted Sobolev space lead to solutions with sharp $L_x^\infty$ decay up to time $\exp(C\varepsilon^{-2})$. We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

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Jason Murphy, Fabio Pusateri. 2016-05-10. Almost global existence for cubic nonlinear Schr\"odinger equations in one space dimension. https://doi.org/10.3934/dcds.2017089

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