Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations. (1st November 2018)

• Record Type: Journal Article
• Authors: Jeong, Eunji; Kim, Junha; Lee, Jihoon
• Other Names: Bianca Carlo Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2018(2018)
• Publication Date: 2018-11-01
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2018/5343824
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without resistivity. Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations.