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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Well-posedness for the fifth-order KdV equation in the energy space
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by Carlos E. Kenig and Didier Pilod PDF
Trans. Amer. Math. Soc. 367 (2015), 2551-2612 Request permission

Abstract:

We prove that the initial value problem (IVP) associated to the fifth-order KdV equation \begin{equation*} \tag {0.1} \partial _tu-\partial ^5_x u=c_1\partial _xu\partial _x^2u+c_2\partial _x(u\partial _x^2u)+c_3\partial _x(u^3), \end{equation*} where $x \in \mathbb R$, $t \in \mathbb R$, $u=u(x,t)$ is a real-valued function and $\alpha , \ c_1, \ c_2, \ c_3$ are real constants with $\alpha \neq 0$, is locally well-posed in $H^s(\mathbb R)$ for $s \ge 2$. In the Hamiltonian case (i.e. when $c_1=c_2$), the IVP associated to (0.1) is then globally well-posed in the energy space $H^2(\mathbb R)$.
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Additional Information
  • Carlos E. Kenig
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 100230
  • Email: cek@math.uchicago.edu
  • Didier Pilod
  • Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, CEP: 21945-970, Rio de Janeiro, RJ, Brazil
  • MR Author ID: 837520
  • Email: didier@im.ufrj.br
  • Received by editor(s): May 3, 2012
  • Received by editor(s) in revised form: June 23, 2012, and October 6, 2012
  • Published electronically: December 4, 2014
  • Additional Notes: The first author was partially supported by NSF Grant DMS-0968472
    The second author was partially supported by CNPq/Brazil, Grant 200001/2011-6
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 2551-2612
  • MSC (2010): Primary 35Q53, 35Q35, 35A01; Secondary 37K05, 76B15
  • DOI: https://doi.org/10.1090/S0002-9947-2014-05982-5
  • MathSciNet review: 3301874