Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem

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dc.contributor.authorRoman, Carlos
dc.contributor.authorSandier, Etienne
dc.contributor.authorSerfaty, Sylvia
dc.date.accessioned2025-01-20T20:07:06Z
dc.date.available2025-01-20T20:07:06Z
dc.date.issued2023
dc.description.abstractWe consider the full three-dimensional Ginzburg-Landau model of superconductivity with applied magnetic field, in the regime where the intensity of the applied field is close to the 'first critical field' Hc1$H_{c_1}$ at which vortex filaments appear, and in the asymptotics of a small inverse Ginzburg-Landau parameter epsilon$\varepsilon$. This onset of vorticity is directly related to an 'isoflux problem' on curves (finding a curve that maximizes the ratio of a magnetic flux by its length), whose study was initiated in [22] and which we continue here. By assuming a nondegeneracy condition for this isoflux problem, which we show holds at least for instance in the case of a ball, we prove that if the intensity of the applied field remains below Hc1+Clog|log epsilon|${H_{c_1}}+ C \log {|\log \varepsilon |}$, the total vorticity remains bounded independently of epsilon$\varepsilon$, with vortex lines concentrating near the maximizer of the isoflux problem, thus extending to the three-dimensional setting a two-dimensional result of [28]. We finish by showing an improved estimate on the value of Hc1${H_{c_1}}$ in some specific simple geometries.
dc.fuente.origenWOS
dc.identifier.doi10.1112/plms.12505
dc.identifier.eissn1460-244X
dc.identifier.issn0024-6115
dc.identifier.urihttps://doi.org/10.1112/plms.12505
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91765
dc.identifier.wosidWOS:000907276200001
dc.issue.numero3
dc.language.isoen
dc.pagina.final1062
dc.pagina.inicio1015
dc.revistaProceedings of the london mathematical society
dc.rightsacceso restringido
dc.titleBounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem
dc.typeartículo
dc.volumen126
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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