Self-similar dynamics for the modified Korteweg-de Vries equation
Analysis of PDEs
2019-04-10 v1
Abstract
We prove a local well posedness result for the modified Korteweg-de Vries equation in a critical space designed so that is contains self-similar solutions. As a consequence, we can study the flow of this equation around self-similar solutions: in particular, we give an as-ymptotic description of small solutions as t + and construct solutions with a prescribed blow up behavior as t 0.
Cite
@article{arxiv.1904.04524,
title = {Self-similar dynamics for the modified Korteweg-de Vries equation},
author = {Simão Correia and Raphaël Côte and Luis Vega},
journal= {arXiv preprint arXiv:1904.04524},
year = {2019}
}