We show that the recent work by Gérard–Kappeler–Topalov can be used in order to construct new non degenerate invariant measures for the Benjamin–Ono equation on the Sobolev spaces , .
Révisé le :
Accepté le :
Publié le :
Nikolay Tzvetkov 1
![](/mathematique/static/ptf/img/CC-BY%204.0.png)
@article{CRMATH_2024__362_G1_77_0, author = {Nikolay Tzvetkov}, title = {New non degenerate invariant measures for the {Benjamin{\textendash}Ono} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {77--86}, publisher = {Acad\'emie des sciences, Paris}, volume = {362}, year = {2024}, doi = {10.5802/crmath.536}, language = {en}, }
Nikolay Tzvetkov. New non degenerate invariant measures for the Benjamin–Ono equation. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 77-86. doi : 10.5802/crmath.536. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.536/
[1] Random data Cauchy theory for supercritical wave equations. I. Local theory, Invent. Math., Volume 173 (2008) no. 3, pp. 449-475 | DOI | MR | Zbl
[2] Probabilistic well-posedness for the cubic wave equation, J. Eur. Math. Soc., Volume 16 (2014) no. 1, pp. 1-30 | DOI | MR | Zbl
[3] Invariance of the Gibbs measure for the Benjamin-Ono equation, J. Eur. Math. Soc., Volume 17 (2015) no. 5, pp. 1107-1198 | DOI | MR | Zbl
[4] Invariant measures and long time behaviour for the Benjamin-Ono equation III, Commun. Math. Phys., Volume 339 (2015) no. 3, pp. 815-857 | DOI | MR | Zbl
[5] On the integrability of the Benjamin-Ono equation on the torus, Commun. Pure Appl. Math., Volume 74 (2021) no. 8, pp. 1685-1747 | DOI | MR | Zbl
[6] Sharp well-posedness results of the Benjamin-Ono equation in and qualitative properties of its solution (2020) | arXiv
[7] Sharp well-posedness for the Benjamin–Ono equation (2023) | arXiv
[8] Invariance of the white noise for KdV, Commun. Math. Phys., Volume 292 (2009) no. 1, pp. 217-236 | MR | Zbl
[9] Real analysis. Measure theory, integration, and Hilbert spaces, Princeton Lectures in Analysis, 3, Princeton University Press, 2005, xix+402 pages | DOI
[10] Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation, Probab. Theory Relat. Fields, Volume 146 (2010) no. 3-4, pp. 481-514 | DOI | MR | Zbl
[11] EDP non linéaires en présence d’aléa singulier, Gaz. Math., Soc. Math. Fr., Volume 160 (2019), pp. 6-14 | Zbl
[12] Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation, Ann. Sci. Éc. Norm. Supér., Volume 46 (2013) no. 2, pp. 249-299 | DOI | Numdam | MR | Zbl
[13] Invariant measures and long time behaviour for the Benjamin-Ono equation, Int. Math. Res. Not., Volume 2014 (2014) no. 17, p. 4679-4614 | DOI | Zbl
[14] Invariant measures and long time behaviour for the Benjamin-Ono equation II, J. Math. Pures Appl., Volume 109 (2014) no. 1, pp. 102-141 | MR
Cité par Sources :
Commentaires - Politique