On the one dimensional cubic NLS in a critical space-Reference-Cited by-同舟云学术

On the one dimensional cubic NLS in a critical space

Published:2022 Issue:6 Volume:42 Page:2563
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Bravin Marco¹,Vega Luis¹

Affiliation:

1. BCAM - Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Basque Country - Spain

Abstract

<p style='text-indent:20px;'>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference20 articles.

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4. J. Bourgain.Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Geom. Funct. Anal., 3 (1993), 209-262.

5. R. Carles, T. Kappeler.Norm-inflation with infinite loss of regularity for periodic NLS equations in negative Sobolev spaces, Bull. Soc. Math. France, 145 (2017), 623-642.

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