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Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation
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  • Published: 13 January 2009

Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation

  • N. Tzvetkov1 

Probability Theory and Related Fields volume 146, pages 481–514 (2010)Cite this article

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Abstract

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin–Ono equation, posed on the circle, on the first N, N ≥ 1 modes in the trigonometric bases.

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Authors and Affiliations

  1. Département de Mathématiques, Université Lille I, 59 655, Villeneuve d’Ascq Cedex, France

    N. Tzvetkov

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  1. N. Tzvetkov
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Correspondence to N. Tzvetkov.

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Cite this article

Tzvetkov, N. Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation. Probab. Theory Relat. Fields 146, 481–514 (2010). https://doi.org/10.1007/s00440-008-0197-z

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  • Received: 26 May 2008

  • Revised: 21 November 2008

  • Published: 13 January 2009

  • Issue Date: March 2010

  • DOI: https://doi.org/10.1007/s00440-008-0197-z

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Keywords

  • Dispersive equations
  • Invariant measures

Mathematics Subject Classification (2000)

  • 35Q55
  • 35BXX
  • 37K05
  • 37L50
  • 81Q20
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