Global Well-posedness in L for the Periodic Benjamin-ono Equation

  title={Global Well-posedness in L for the Periodic Benjamin-ono Equation},
  author={Luc Molinet},
We prove that the Benjamin-Ono equation is globally well-posed in Hs(T) for s ≥ 0. Moreover we show that the associated flow-map is Lipschitz on every bounded set of Hs 0 (T), s ≥ 0, and even real-analytic in this space for small times. This result is sharp in the sense that the flow-map (if it can be defined and coincides with the standard flow-map on H∞ 0 (T)) cannot be of class C , α > 0, from Hs 0(T) into H s 0(T) as soon as s < 0. 
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Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I

  • J. Bourgain
  • The Schrödinger equation, GAFA,
  • 1993
Highly Influential
18 Excerpts

Nonlocal models for nonlinear, dispersive waves

  • L. Abdelouhab, J. Bona, M. Felland, J. C. Saut
  • Phys. D
  • 1989
Highly Influential
10 Excerpts

On the Cauchy problem for the Benjamin-Ono equation, Comm

  • J. R. Iorio
  • Partial Differential Equations
  • 1986
Highly Influential
4 Excerpts

On well-posedness for the Benjamin

  • N. Burq, F. Planchon
  • Ono equation,
  • 2005
2 Excerpts

On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono

  • C. E. Kenig, K. Koenig
  • equations, Math. Res. Lett
  • 2003
1 Excerpt

On the local well-posedness of the Benjamin-Ono equation in Hs(IR), IMRN

  • H. Koch, N. Tzvetkov
  • 2003
1 Excerpt

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