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arXiv · 1904.04524

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

Simão Correia·Raphaël Côte·Luis Vega
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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 $\rightarrow$ +$\infty$ and construct solutions with a prescribed blow up behavior as t $\rightarrow$ 0.

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Simão Correia, Raphaël Côte, Luis Vega. 2019-04-09. Self-similar dynamics for the modified Korteweg-de Vries equation. https://arxiv.org/abs/1904.04524

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