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

Yvan Martel; Frank Merle; Pierre Raphaël

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 8, page 1855-1925
- ISSN: 1435-9855

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topMartel, 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 -

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