Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
[Mesures gaussiennes associées à une loi de conservation arbitraire de l'équation de Benjamin-Ono]
Tzvetkov, Nikolay ; Visciglia, Nicola
Annales scientifiques de l'École Normale Supérieure, Tome 46 (2013), p. 249-299 / Harvested from Numdam
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Inspirés par le travail de Zhidkov sur l'équation KdV, nous construisons des mesures gaussiennes à poids associées à une loi de conservation arbitraire de l'équation de Benjamin-Ono. Les supports de ces mesures sont constitués de fonctions de régularité de Sobolev croissantes. On démontre aussi une propriété-clé des mesures qui nous conduit à conjecturer leur invariance par le flot de l'équation.

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.

Publié le : 2013-01-01
DOI : https://doi.org/10.24033/asens.2189
Classification:  35Q35,  37L40,  28C20
Mots clés: Équations dispersives, chaos de Wiener, mesures invariantes 
@article{ASENS_2013_4_46_2_249_0,
     author = {Tzvetkov, Nikolay and Visciglia, Nicola},
     title = {Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {46},
     year = {2013},
     pages = {249-299},
     doi = {10.24033/asens.2189},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2013_4_46_2_249_0}
}

Tzvetkov, Nikolay; Visciglia, Nicola. Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. Annales scientifiques de l'École Normale Supérieure, Tome 46 (2013) pp. 249-299. doi : 10.24033/asens.2189. http://gdmltest.u-ga.fr/item/ASENS_2013_4_46_2_249_0/

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