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

We prove a local well posedness result for the modified Korteweg-de Vries equa- tion 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...

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Detalles Bibliográficos
Autores: Correia, S., Côte, R., Vega, L.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1081
Acceso en línea:http://hdl.handle.net/20.500.11824/1081
Access Level:acceso abierto
Descripción
Sumario:We prove a local well posedness result for the modified Korteweg-de Vries equa- tion 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.