dc.contributor.author | Galimberti, Luca | |
dc.contributor.author | Holden, Helge | |
dc.contributor.author | Karlsen, Kenneth Aksel Hvistendahl | |
dc.contributor.author | Pang, Ho Cheung | |
dc.date.accessioned | 2024-01-18T13:00:54Z | |
dc.date.available | 2024-01-18T13:00:54Z | |
dc.date.created | 2023-12-25T10:21:03Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Journal of Differential Equations. 2023, 387 1-103. | en_US |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | https://hdl.handle.net/11250/3112523 | |
dc.description.abstract | We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa–Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for dissipative weak martingale solutions to this SPDE, with general finite-energy initial data. The solution is obtained as the limit of classical solutions to parabolic SPDEs. The proof combines model-specific statistical estimates with stochastic propagation of compactness techniques, along with the systematic use of tightness and a.s. representations of random variables on specific quasi-Polish spaces. The spatial dependence of the noise function makes more difficult the analysis of a priori estimates and various renormalisations, giving rise to nonlinear terms induced by the martingale part of the equation and the second-order Stratonovich–Itô correction term. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Elsevier B. V. | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Global existence of dissipative solutions to the Camassa--Holm equation with transport noise | en_US |
dc.title.alternative | Global existence of dissipative solutions to the Camassa--Holm equation with transport noise | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | submittedVersion | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.pagenumber | 1-103 | en_US |
dc.source.volume | 387 | en_US |
dc.source.journal | Journal of Differential Equations | en_US |
dc.identifier.doi | 10.1016/j.jde.2023.12.021 | |
dc.identifier.cristin | 2217509 | |
dc.relation.project | Norges forskningsråd: 301538 | en_US |
dc.relation.project | Norges forskningsråd: 250070 | en_US |
dc.relation.project | Norges forskningsråd: 325114 | en_US |
cristin.ispublished | false | |
cristin.fulltext | preprint | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |