Blow up for the critical gKdV equation. II: Minimal mass dynamics

Martel, Yvan, Merle, Frank, and Raphaël, Pierre. "Blow up for the critical gKdV equation. II: Minimal mass dynamics." Journal of the European Mathematical Society 017.8 (2015): 1855-1925. <http://eudml.org/doc/277329>.

@article{Martel2015,
abstract = {We consider the mass critical (gKdV) equation $u_t + (u_\{xx\} + u^5)_x =0$ for initial data in $H^1$. 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].},
author = {Martel, Yvan, Merle, Frank, Raphaël, Pierre},
journal = {Journal of the European Mathematical Society},
keywords = {generalized Korteweg–de Vries equation; blow up; minimal mass solution; uniqueness of threshold solution; generalized Korteweg-de Vries equation; blow up; minimal mass solution; uniqueness of threshold solution},
language = {eng},
number = {8},
pages = {1855-1925},
publisher = {European Mathematical Society Publishing House},
title = {Blow up for the critical gKdV equation. II: Minimal mass dynamics},
url = {http://eudml.org/doc/277329},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Martel, Yvan
AU - Merle, Frank
AU - Raphaël, Pierre
TI - Blow up for the critical gKdV equation. II: Minimal mass dynamics
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 8
SP - 1855
EP - 1925
AB - We consider the mass critical (gKdV) equation $u_t + (u_{xx} + u^5)_x =0$ for initial data in $H^1$. 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].
LA - eng
KW - generalized Korteweg–de Vries equation; blow up; minimal mass solution; uniqueness of threshold solution; generalized Korteweg-de Vries equation; blow up; minimal mass solution; uniqueness of threshold solution
UR - http://eudml.org/doc/277329
ER -