Self-similar dynamics for the modified Korteweg-de Vries equation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Mathematics Research Notices Année : 2021

Self-similar dynamics for the modified Korteweg-de Vries equation

Résumé

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.
Fichier principal
Vignette du fichier
mkdv_critical_v11.pdf (186.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02092626 , version 1 (08-04-2019)
hal-02092626 , version 2 (07-01-2022)

Identifiants

Citer

Simão Correia, Raphaël Côte, Luis Vega. Self-similar dynamics for the modified Korteweg-de Vries equation. International Mathematics Research Notices, 2021, 2021 (13), pp.9958-10013. ⟨10.1093/imrn/rnz383⟩. ⟨hal-02092626v2⟩
53 Consultations
78 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More