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arXiv · 2107.01934

On the one dimensional cubic NLS in a critical space

Marco Bravin·Luis Vega
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Abstract

In this note we study the initial value problem in a critical space for the one dimensional Schr\"odinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.

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Marco Bravin, Luis Vega. 2021-07-05. On the one dimensional cubic NLS in a critical space. https://arxiv.org/abs/2107.01934

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