Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation
Raphaël Côte1
1 Université de Strasbourg CNRS, IRMA UMR 7501 F-67000 Strasbourg, France
Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 4, 15 p.

We present some results obtained in collaboration with Simão Correia (University of Lisbon) and Luis Vega (University of Bilbao), regarding the understanding of self-similar solutions for the modified Korteweg-de Vries equation (mKdV). We obtain the description of self-similar solutions in Fourier space, and we also prove a local well-posedness result in a critical space where self-similar solutions live. As a consequence, we can study the flow of (mKdV) around self-similar solutions: in particular, we give an asymptotic description of small solutions as t→+∞ and construct solutions with a prescribed blow up behavior as t→0.

Published online:
DOI: 10.5802/slsedp.130
Raphaël Côte 1

1 Université de Strasbourg CNRS, IRMA UMR 7501 F-67000 Strasbourg, France 
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Raphaël Côte. Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Talk no. 4, 15 p. doi : 10.5802/slsedp.130. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.130/

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