Blow up and near soliton dynamics for the L 2 critical gKdV equation
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 37, 14 p.

These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation u t +(u xx +u 5 ) x =0 for initial data in H 1 close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in H 1 , construction of various exotic blow up rates in H 1 , including grow up in infinite time.

DOI : 10.5802/slsedp.28
Martel, Yvan 1 ; Merle, Frank 2 ; Raphaël, Pierre 3

1 Université de Versailles St-Quentin and Institut Universitaire de France LMV CNRS UMR8100
2 Université de Cergy Pontoise and Institut des Hautes Études Scientifiques, AGM CNRS UMR8088
3 Université Paul Sabatier and Institut Universitaire de France, IMT CNRS UMR 5219
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Martel, Yvan; Merle, Frank; Raphaël, Pierre. Blow up and near soliton dynamics for the $L^2$ critical gKdV equation. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 37, 14 p. doi : 10.5802/slsedp.28. http://www.numdam.org/articles/10.5802/slsedp.28/

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