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]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 46 (2013) no. 2, pp. 249-299.

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.

DOI : 10.24033/asens.2189
Classification : 35Q35, 37L40, 28C20
Keywords: dispersive equations, Wiener chaos, invariant measures
Mot clés : Équations dispersives, chaos de Wiener, mesures invariantes 
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     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},
     pages = {249--299},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 46},
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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, Série 4, Tome 46 (2013) no. 2, pp. 249-299. doi : 10.24033/asens.2189. https://www.numdam.org/articles/10.24033/asens.2189/

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