Open AccessOn the one dimensional cubic NLS in a critical space
Author(s) -
Marco Bravin,
Luis Vega
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021203
Subject(s) - space (punctuation) , curvature , mathematical analysis , amplitude , initial value problem , mathematics , flow (mathematics) , physics , linearity , cubic function , sequence (biology) , mathematical physics , geometry , computer science , quantum mechanics , operating system , biology , genetics
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.