On the one dimensional cubic NLS in a critical space

2021/07/05 by Bravin, Marco, Vega, Luis
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.01934

Abstract

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.

Related

• Singularity formation for the 1-D cubic NLS and the Schr "odinger map on\n mathbb S²
• A new class of critical solutions for 1D cubic NLS
• On the 1D Cubic Nonlinear Schrodinger Equation in an Almost Critical Space
• A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces
• Blow-up for the 1D cubic NLS