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arXiv · 1706.08475

Local Cauchy theory for the nonlinear Schr\"odinger equation in spaces of infinite mass

Simão Correia
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Abstract

We consider the Cauchy problem for the nonlinear Schr\"odinger equation on $\mathbb{R}^d$, where the initial data is in $\dot{H}^1(\mathbb{R}^d)\cap L^p(\mathbb{R}^d)$. We prove local well-posedness for large ranges of $p$ and discuss some global well-posedness results.

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Simão Correia. 2017-06-26. Local Cauchy theory for the nonlinear Schr\"odinger equation in spaces of infinite mass. https://arxiv.org/abs/1706.08475

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