On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation

Carlos E. Kenig; Felipe Linares; Gustavo Ponce; Luis Vega

On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation

Analysis of PDEs 2016-09-27 v2

Authors: Carlos E. Kenig , Felipe Linares , Gustavo Ponce , Luis Vega

Abstract

This work is concerned with special regularity properties of solutions to the $k$ -generalized Korteweg-de Vries equation. In \cite{IsazaLinaresPonce} it was established that if the initial datun $u_0\in H^l((b,\infty))$ for some $l\in\mathbb Z^+$ and $b\in \mathbb R$ , then the corresponding solution $u(\cdot,t)$ belongs to $H^l((\beta,\infty))$ for any $\beta \in \mathbb R$ and any $t\in (0,T)$ . Our goal here is to extend this result to the case where $\,l\in \mathbb R^+$ .

Keywords

k-generalized Korteweg-de Vries equation regularity of solutions initial data Sobolev spaces

Cite

@article{arxiv.1606.03715,
  title  = {On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation},
  author = {Carlos E. Kenig and Felipe Linares and Gustavo Ponce and Luis Vega},
  journal= {arXiv preprint arXiv:1606.03715},
  year   = {2016}
}

On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation

Abstract

Keywords

Cite

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