dc.date.accessioned | 2024-01-15T17:53:06Z | |
dc.date.available | 2024-01-15T17:53:06Z | |
dc.date.created | 2023-12-25T10:21:03Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Galimberti, Luca Holden, Helge Karlsen, Kenneth Aksel Hvistendahl Pang, Ho Cheung . Global existence of dissipative solutions to the Camassa--Holm equation with transport noise. Journal of Differential Equations. 2023, 387, 1-103 | |
dc.identifier.uri | http://hdl.handle.net/10852/106823 | |
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. | |
dc.language | EN | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | Global existence of dissipative solutions to the Camassa--Holm equation with transport noise | |
dc.title.alternative | ENEngelskEnglishGlobal existence of dissipative solutions to the Camassa--Holm equation with transport noise | |
dc.type | Journal article | |
dc.creator.author | Galimberti, Luca | |
dc.creator.author | Holden, Helge | |
dc.creator.author | Karlsen, Kenneth Aksel Hvistendahl | |
dc.creator.author | Pang, Ho Cheung | |
cristin.unitcode | 185,15,13,45 | |
cristin.unitname | Differensiallikninger og beregningsorientert matematikk | |
cristin.ispublished | false | |
cristin.fulltext | preprint | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 2217509 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal of Differential Equations&rft.volume=387&rft.spage=1&rft.date=2023 | |
dc.identifier.jtitle | Journal of Differential Equations | |
dc.identifier.volume | 387 | |
dc.identifier.startpage | 1 | |
dc.identifier.endpage | 103 | |
dc.identifier.doi | https://doi.org/10.1016/j.jde.2023.12.021 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0022-0396 | |
dc.type.version | PublishedVersion | |
dc.relation.project | NFR/301538 | |
dc.relation.project | NFR/250070 | |
dc.relation.project | NFR/325114 | |