dc.creator | Chae, Dongho | es |
dc.creator | Constantin, Peter | es |
dc.creator | Córdoba Gazolaz, Diego | es |
dc.creator | Gancedo García, Francisco | es |
dc.creator | Wu, Jiahong | es |
dc.date.accessioned | 2016-09-21T10:55:16Z | |
dc.date.available | 2016-09-21T10:55:16Z | |
dc.date.issued | 2012 | |
dc.identifier.citation | Chae, D., Constantin, P., Córdoba Gazolaz, D., Gancedo García, F. y Wu, J. (2012). Generalized surface quasi-geostrophic equations with singular velocities. Communications on Pure and Applied Mathematics, 65 (8), 1037-1066. | |
dc.identifier.issn | 0010-3640 | es |
dc.identifier.issn | 1097-0312 | es |
dc.identifier.uri | http://hdl.handle.net/11441/45197 | |
dc.description.abstract | This paper establishes several existence and uniqueness results for two
families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasi-geostrophic (SQG) equation with the velocity field u related to the scalar θ by u = ∇⊥Λ β−2 θ, where 1 < β ≤ 2 and Λ = (−∆)1/2 is the Zygmund operator. The borderline case β = 1 corresponds to the SQG equation and the situation is more singular for β > 1. We obtain the local existence and uniqueness of classical solutions, the global existence of
weak solutions and the local existence of patch type solutions. The second family is a dissipative active scalar equation with u = ∇⊥(log(I − ∆))µθ for µ > 0, which is at least logarithmically more singular than the velocity in the first family. We prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data. This result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by K. Ohkitani. | es |
dc.description.sponsorship | National Research Foundation of Korea | es |
dc.description.sponsorship | National Science Foundation | es |
dc.description.sponsorship | Ministerio de Ciencia e Innovación | es |
dc.description.sponsorship | European Research Council | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | Wiley | es |
dc.relation.ispartof | Communications on Pure and Applied Mathematics, 65 (8), 1037-1066. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Generalized surface quasi-geostrophic equation | es |
dc.subject | Active scalar equation | es |
dc.subject | Existence and uniqueness | es |
dc.title | Generalized surface quasi-geostrophic equations with singular velocities | es |
dc.type | info:eu-repo/semantics/article | es |
dc.type.version | info:eu-repo/semantics/submittedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Análisis Matemático | es |
dc.relation.projectID | 2006-0093854 | es |
dc.relation.projectID | DMS 0804380 | es |
dc.relation.projectID | MTM2008-03754 | es |
dc.relation.projectID | info:eu-repo/grantAgreement/EC/FP7/203138 | es |
dc.relation.projectID | DMS-0901810 | es |
dc.relation.publisherversion | http://onlinelibrary.wiley.com/doi/10.1002/cpa.21390/epdf | es |
dc.identifier.doi | 10.1002/cpa.21390 | es |
dc.contributor.group | Universidad de Sevilla. FQM104: Analisis Matematico | es |
idus.format.extent | 29 p. | es |
dc.journaltitle | Communications on Pure and Applied Mathematics | es |
dc.publication.volumen | 65 | es |
dc.publication.issue | 8 | es |
dc.publication.initialPage | 1037 | es |
dc.publication.endPage | 1066 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/45197 | |