Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schr\"odinger Equation
Analysis of PDEs
2020-12-21 v1
Abstract
A polynomial-in-time growth bound is established for global Sobolev solutions to the derivative nonlinear Schr\"odinger equation on the circle with . 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.
Keywords
Cite
@article{arxiv.2012.09933,
title = {Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schr\"odinger Equation},
author = {Bradley Isom and Dionyssios Mantzavinos and Atanas Stefanov},
journal= {arXiv preprint arXiv:2012.09933},
year = {2020}
}