Geodesic
Blow up for the critical gKdV equation. II: Minimal mass dynamics
Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1855-1925.

Voir la notice de l'article provenant de la source EMS Press

We consider the mass critical (gKdV) equation ut​+(uxx​+u5)x​=0 for initial data in H1. We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
DOI : 10.4171/jems/547
Classification : 35-XX
Keywords: Generalized Korteweg–de Vries equation, blow up, minimal mass solution, uniqueness of threshold solution 
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     title = {Blow up for the critical {gKdV} equation. {II:} {Minimal} mass dynamics},
     journal = {Journal of the European Mathematical Society},
     pages = {1855--1925},
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Yvan Martel; Frank Merle; Pierre Raphaël. Blow up for the critical gKdV equation. II: Minimal mass dynamics. Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 1855-1925. doi : 10.4171/jems/547. http://geodesic.mathdoc.fr/articles/10.4171/jems/547/

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