dc.date.accessioned | 2023-03-03T18:28:30Z | |
dc.date.available | 2023-03-03T18:28:30Z | |
dc.date.created | 2022-11-15T08:21:11Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Holden, Helge Karlsen, Kenneth Aksel Hvistendahl Pang, Ho Cheung . Global well-posedness of the viscous Camassa–Holm equation with gradient noise. Discrete and Continuous Dynamical Systems. Series A. 2022, 43(2), 568-618 | |
dc.identifier.uri | http://hdl.handle.net/10852/100678 | |
dc.description.abstract | We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa–Holm type) perturbed by a convective, position-dependent noise term. We establish the existence of weak solutions in Hm (m∈N) using Galerkin approximations and the stochastic compactness method. We derive a series of a priori estimates that combine a model-specific energy law with non-standard regularity estimates. We make systematic use of a stochastic Gronwall inequality and also stopping time techniques. The proof of convergence to a solution argues via tightness of the laws of the Galerkin solutions, and Skorokhod–Jakubowski a.s. representations of random variables in quasi-Polish spaces. The spatially dependent noise function constitutes a complication throughout the analysis, repeatedly giving rise to nonlinear terms that "balance" the martingale part of the equation against the second-order Stratonovich-to-Itô correction term. Finally, via pathwise uniqueness, we conclude that the constructed solutions are probabilistically strong. The uniqueness proof is based on a finite-dimensional Itô formula and a DiPerna–Lions type regularisation procedure, where the regularisation errors are controlled by first and second order commutators. | |
dc.language | EN | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.title | Global well-posedness of the viscous Camassa–Holm equation with gradient noise | |
dc.title.alternative | ENEngelskEnglishGlobal well-posedness of the viscous Camassa–Holm equation with gradient noise | |
dc.type | Journal article | |
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 | Beregningsorientert matematikk | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.fulltext | preprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 2073918 | |
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=Discrete and Continuous Dynamical Systems. Series A&rft.volume=43&rft.spage=568&rft.date=2022 | |
dc.identifier.jtitle | Discrete and Continuous Dynamical Systems. Series A | |
dc.identifier.volume | 43 | |
dc.identifier.issue | 2 | |
dc.identifier.startpage | 568 | |
dc.identifier.endpage | 618 | |
dc.identifier.doi | https://doi.org/10.3934/dcds.2022163 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 1078-0947 | |
dc.type.version | PublishedVersion | |
dc.type.version | SubmittedVersion | |
dc.relation.project | NFR/250070 | |
dc.relation.project | NFR/301538 | |