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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Blow up in finite time and dynamics of blow up solutions for the $L^2$–critical generalized KdV equation
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by Yvan Martel and Frank Merle PDF
J. Amer. Math. Soc. 15 (2002), 617-664 Request permission

Abstract:

In this paper, we describe the dynamics of blow up solutions for the critical generalized KdV equation such that the initial data is close to the soliton in $L^2$ and has decay in $L^2$ at the right. In particular, we prove that blow up occurs in finite time, and we obtain an upper bound on the blow up rate.
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Additional Information
  • Yvan Martel
  • Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France
  • MR Author ID: 367956
  • Email: Yvan.Martel@math.u-cergy.fr
  • Frank Merle
  • Affiliation: Département de Mathématiques, Université de Cergy–Pontoise, 2, av. A. Chauvin, 95302 Cergy Pontoise, France – and – Institut Universitaire de France
  • MR Author ID: 123710
  • Email: Frank.Merle@math.u-cergy.fr
  • Received by editor(s): March 15, 2001
  • Published electronically: March 8, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 15 (2002), 617-664
  • MSC (1991): Primary 35Q53; Secondary 35B05, 35Q51
  • DOI: https://doi.org/10.1090/S0894-0347-02-00392-2
  • MathSciNet review: 1896235