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 
@article{JEMS_2015_17_8_a1,
     author = {Yvan Martel and Frank Merle and Pierre Rapha\"el},
     title = {Blow up for the critical {gKdV} equation. {II:} {Minimal} mass dynamics},
     journal = {Journal of the European Mathematical Society},
     pages = {1855--1925},
     publisher = {mathdoc},
     volume = {17},
     number = {8},
     year = {2015},
     doi = {10.4171/jems/547},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/547/}
}
TY  - JOUR
AU  - Yvan Martel
AU  - Frank Merle
AU  - Pierre Raphaël
TI  - Blow up for the critical gKdV equation. II: Minimal mass dynamics
JO  - Journal of the European Mathematical Society
PY  - 2015
SP  - 1855
EP  - 1925
VL  - 17
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/547/
DO  - 10.4171/jems/547
ID  - JEMS_2015_17_8_a1
ER  - 
%0 Journal Article
%A Yvan Martel
%A Frank Merle
%A Pierre Raphaël
%T Blow up for the critical gKdV equation. II: Minimal mass dynamics
%J Journal of the European Mathematical Society
%D 2015
%P 1855-1925
%V 17
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/547/
%R 10.4171/jems/547
%F JEMS_2015_17_8_a1
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

Cité par Sources :