Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation

Nikolay Tzvetkov; Nicola Visciglia

Annales scientifiques de l'École Normale Supérieure (2013)

  • Volume: 46, Issue: 2, page 249-299
  • ISSN: 0012-9593

Abstract

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Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.

How to cite

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Tzvetkov, Nikolay, and Visciglia, Nicola. "Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation." Annales scientifiques de l'École Normale Supérieure 46.2 (2013): 249-299. <http://eudml.org/doc/272128>.

@article{Tzvetkov2013,
abstract = {Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.},
author = {Tzvetkov, Nikolay, Visciglia, Nicola},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {dispersive equations; Wiener chaos; invariant measures},
language = {eng},
number = {2},
pages = {249-299},
publisher = {Société mathématique de France},
title = {Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation},
url = {http://eudml.org/doc/272128},
volume = {46},
year = {2013},
}

TY - JOUR
AU - Tzvetkov, Nikolay
AU - Visciglia, Nicola
TI - Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2013
PB - Société mathématique de France
VL - 46
IS - 2
SP - 249
EP - 299
AB - Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
LA - eng
KW - dispersive equations; Wiener chaos; invariant measures
UR - http://eudml.org/doc/272128
ER -

References

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