Local well-posedness and blow-up for the solutions to the axisymmetric inviscid Hall-MHD equations
type: Item
instance of: scholarly article
title: Local well-posedness and blow-up for the solutions to the axisymmetric inviscid Hall-MHD equations
zbMATH Open document ID: 1404.35064
DOI: 10.1155/2018/5343824
author: Eunji Jeong
author: Junha Kim
author: Jihoon Lee
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 6991979
zbMATH Keywords: regularity problem
zbMATH Keywords: incompressible Hall-magnetohydrodynamics equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5343824
OpenAlex ID: W2898875111
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Wikidata QID: Q129009302
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description: scientific article; zbMATH DE number 6991979