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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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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DOI: https://doi.org/10.1007/s00440-008-0197-z
Keywords
- Dispersive equations
- Invariant measures
Mathematics Subject Classification (2000)
- 35Q55
- 35BXX
- 37K05
- 37L50
- 81Q20