Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations

Eunji Jeong, Junha Kim and Jihoon Lee

Advances in Mathematical Physics, 2018, vol. 2018, 1-16

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5343824

DOI: 10.1155/2018/5343824

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