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Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton

Yvan Martel Université de Versailles St-Quentin and Institut Universitaire de France, LMV CNRS UMR8100, Versailles Cedex, France Frank Merle Université de Cergy Pontoise and Institut des Hautes Études Scientifiques, AGM CNRS UMR8088, Paris, France Pierre Raphaël Université Paul Sabatier and Institut Universitaire de France, IMT CNRS UMR 5219, Toulouse, France

Analysis of PDEs mathscidoc:1701.03012

Acta Mathematica, 212, (1), 59-140, 2012.2
We consider the quintic generalized Korteweg–de Vries equation (gKdV) $$u_t + (u_{xx} + u^5)_x =0,$$ which is a canonical mass critical problem, for initial data in$H$^{1}close to the soliton. In earlier works on this problem, finite- or infinite-time blow up was proved for non-positive energy solutions, and the solitary wave was shown to be the universal blow-up profile, see [16], [26] and [20]. For well-localized initial data, finite-time blow up with an upper bound on blow-up rate was obtained in [18].
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@inproceedings{yvan2012blow,
  title={Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton},
  author={Yvan Martel, Frank Merle, and Pierre Raphaël},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402439885785},
  booktitle={Acta Mathematica},
  volume={212},
  number={1},
  pages={59-140},
  year={2012},
}
Yvan Martel, Frank Merle, and Pierre Raphaël. Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton. 2012. Vol. 212. In Acta Mathematica. pp.59-140. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402439885785.
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