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

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.
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https://hal.archives-ouvertes.fr/hal-02092626
Contributor : Raphaël Côte <>
Submitted on : Monday, April 8, 2019 - 12:03:28 PM
Last modification on : Thursday, April 11, 2019 - 1:18:05 AM

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  • HAL Id : hal-02092626, version 1
  • ARXIV : 1904.04524

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Simão Correia, Raphaël Côte, Luis Vega. Self-similar dynamics for the modified Korteweg-de Vries equation. 2019. ⟨hal-02092626⟩

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