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, issue 1

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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https://doi.org/10.1155/2018/5343824

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:5343824

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