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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.
  • Abstract

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.

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Published online: 2019-05-09
DOI: 10.5802/slsedp.130
Author's affiliations:
Raphaël Côte 1

1 Université de Strasbourg CNRS, IRMA UMR 7501 F-67000 Strasbourg, France
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@article{SLSEDP_2018-2019____A4_0,
     author = {Rapha\"el C\^ote},
     title = {Self-similar solutions and critical spaces for {the~modified~Korteweg-de} {Vries} equation},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:4},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2018-2019},
     doi = {10.5802/slsedp.130},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.130/}
}
TY  - JOUR
AU  - Raphaël Côte
TI  - Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:4
PY  - 2018-2019
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.130/
DO  - 10.5802/slsedp.130
LA  - en
ID  - SLSEDP_2018-2019____A4_0
ER  - 
%0 Journal Article
%A Raphaël Côte
%T Self-similar solutions and critical spaces for the modified Korteweg-de Vries equation
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:4
%D 2018-2019
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.130/
%R 10.5802/slsedp.130
%G en
%F SLSEDP_2018-2019____A4_0
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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