Non-linear Smoothing for the Periodic Generalized Non-linear Schrödinger Equation

2022/02/28 by McConnell, Ryan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.00098

Abstract

We consider the periodic non-linear Schrödinger equation with non-linearity given by |u|^p-1u for odd p > 1 in dimension 1. We first establish that the difference between the non-linear evolution and a phase rotation of the the linear evolution is in a smoother space. We then study forced and damped defocusing non-linear Schrödinger equations of the above type and establish an analogous smoothing statement that extends globally in time. As a corollary we establish both existence and smootheness for global attractors in the energy space.

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