Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schrödinger Equation

2020/12/17 by Bradley Isom, Isom, Bradley, Dionyssios Mantzavinos +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2012.09933

openalex publication_date 2020/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A polynomial-in-time growth bound is established for global Sobolev H^s(\mathbb T) solutions to the derivative nonlinear Schrödinger equation on the circle with s>1. These bounds are derived as a consequence of a nonlinear smoothing effect for an appropriate gauge-transformed version of the periodic Cauchy problem, according to which a solution with its linear part removed possesses higher spatial regularity than the initial datum associated with that solution.

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