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 :
Tzvetkov, Nikolay  1
CC-BY 4.0
@article{CRMATH_2024__362_G1_77_0,
author = {Tzvetkov, Nikolay},
title = {New non degenerate invariant measures for the {Benjamin{\textendash}Ono} equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {77--86},
year = {2024},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
number = {G1},
doi = {10.5802/crmath.536},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.536/}
}
TY - JOUR AU - Tzvetkov, Nikolay TI - New non degenerate invariant measures for the Benjamin–Ono equation JO - Comptes Rendus. Mathématique PY - 2024 SP - 77 EP - 86 VL - 362 IS - G1 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.536/ DO - 10.5802/crmath.536 LA - en ID - CRMATH_2024__362_G1_77_0 ER -
%0 Journal Article %A Tzvetkov, Nikolay %T New non degenerate invariant measures for the Benjamin–Ono equation %J Comptes Rendus. Mathématique %D 2024 %P 77-86 %V 362 %N G1 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.536/ %R 10.5802/crmath.536 %G en %F CRMATH_2024__362_G1_77_0
Tzvetkov, Nikolay. New non degenerate invariant measures for the Benjamin–Ono equation. Comptes Rendus. Mathématique, Tome 362 (2024) no. G1, pp. 77-86. doi: 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 | Zbl | DOI | MR
[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 | MR | Numdam | 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 :





