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On the one dimensional cubic NLS in a critical space

  • *Corresponding author: Marco Bravin

    *Corresponding author: Marco Bravin 

Marco Bravin is supported by ERC-2014-ADG project HADE Id. 669689 (European Research Council). Luis Vega is supported by ERC-2014-ADG project HADE Id. 669689 (European Research Council), MINECO grant BERC 2018-2021, PGC2018-094522-B-I00 and SEV-2017-0718 (Spain)

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  • In this note we study the initial value problem in a critical space for the one dimensional Schrödinger 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.

    Mathematics Subject Classification: Primary: 35Q55, 34A12, 37L50.


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