Blow up and near soliton dynamics for the L 2 critical gKdV equation

Yvan Martel[1]; Frank Merle[2]; Pierre Raphaël[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

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-14
  • ISSN: 2266-0607

Abstract

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These notes present the main results of [22, 23, 24] concerning the mass critical (gKdV) equation u t + ( u x x + 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.

How to cite

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Martel, Yvan, Merle, Frank, and Raphaël, Pierre. "Blow up and near soliton dynamics for the $L^2$ critical gKdV equation." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-14. <http://eudml.org/doc/251172>.

@article{Martel2011-2012,
abstract = {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.},
affiliation = {Université de Versailles St-Quentin and Institut Universitaire de France LMV CNRS UMR8100; Université de Cergy Pontoise and Institut des Hautes Études Scientifiques, AGM CNRS UMR8088; Université Paul Sabatier and Institut Universitaire de France, IMT CNRS UMR 5219},
author = {Martel, Yvan, Merle, Frank, Raphaël, Pierre},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {blow up},
language = {eng},
pages = {1-14},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Blow up and near soliton dynamics for the $L^2$ critical gKdV equation},
url = {http://eudml.org/doc/251172},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Martel, Yvan
AU - Merle, Frank
AU - Raphaël, Pierre
TI - Blow up and near soliton dynamics for the $L^2$ critical gKdV equation
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 14
AB - 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.
LA - eng
KW - blow up
UR - http://eudml.org/doc/251172
ER -

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