Global regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion

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dc.contributor.authorJin, Meilin
dc.contributor.authorJiu, Quansen
dc.contributor.authorYu, Huan
dc.date.accessioned2025-01-06T17:23:37Z
dc.date.available2025-01-06T17:23:37Z
dc.date.issued2023
dc.departmentAdana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi
dc.description.abstractIn this paper, we study the Cauchy problem for the 3D incompressible axisymmetric Hall-MHD system with horizontal velocity dissipation and vertical magnetic diffusion. We obtain a unique global smooth solution of which in the cylindrical coordinate system the swirl velocity fields, the radial and the vertical components of the magnetic fields are trivial. This type of solution has been studied for the MHD system in [17], [16] and [15] and for the Hall-MHD system with total dissipation and diffusion in [11]. Some new and fine estimates are obtained in this paper to overcome the di?iculties raised from the Hall term and the loss of vertical velocity dissipation and horizontal magnetic diffusion. Finally we can show that the estimates $\\int_{O}^{T}$ ??u(t)?L? dt and $\\int_{O}^{T}$ ??b(t)?L? dt are finite in a priori way and hence obtainthe global well-posedness to the system under considered.
dc.identifier.doi10.55730/1300-0098.3403
dc.identifier.endpage933
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issueSI-1
dc.identifier.startpage910
dc.identifier.trdizinid1190881
dc.identifier.urihttps://doi.org/10.55730/1300-0098.3403
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/1190881
dc.identifier.urihttps://hdl.handle.net/20.500.14669/864
dc.identifier.volume47
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241211
dc.subjectHall-magnetohydrodynamics system
dc.subjectglobal regularity
dc.subjectaxis-symmetric solutions
dc.subjecthorizontal dissipation
dc.subjectver- tical magnetic diffusion
dc.titleGlobal regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion
dc.typeArticle

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