dc.contributor.author
Cantero, J.C.
dc.contributor.author
Mateu, J.
dc.contributor.author
Orobitg, J.
dc.contributor.author
Verdera, J.
dc.date.accessioned
2023-11-14T11:53:19Z
dc.date.accessioned
2024-09-19T14:34:47Z
dc.date.available
2023-11-14T11:53:19Z
dc.date.available
2024-09-19T14:34:47Z
dc.date.issued
2023-09-21
dc.identifier.uri
http://hdl.handle.net/2072/537055
dc.description.abstract
We prove the persistence of boundary smoothness of vortex patches for a nonlinear transport equation in Rn. with velocity field given by convolution of the density with an odd kernel, homogeneous of degree −(n−1) and of class C2(Rn \{0},Rn). This allows the velocity field to have nontrivial divergence. The quasigeostrophic equation in R3 and the Cauchy transport equation in the plane are examples. © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.
eng
dc.description.sponsorship
The authors warmly thank Francisco de la Hoz for a numerical simulation of the ellipses’ evolution; they acknowledge support by 2021-SGR-00071 (Generalitat de Catalunya) and PID2020-112881GB-I00. Mateu, Orobitg and Verdera are supported by the Severo Ochoa and Maria de Maeztu centers of excellence CEX2020-001084-M.
dc.format.extent
27 p.
cat
dc.publisher
Mathematical Sciences Publishers
cat
dc.relation.ispartof
Analysis & PDE
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Potential theory; transport equation; vortex patch
cat
dc.title
THE REGULARITY OF THE BOUNDARY OF VORTEX PATCHES FOR SOME NONLINEAR TRANSPORT EQUATIONS
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/acceptedVersion
cat
dc.identifier.doi
10.2140/apde.2023.16.1621
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
