On the formation of singularities in magnetohydrodynamic waves
type: Item
instance of: scholarly article
title: On the formation of singularities in magnetohydrodynamic waves
zbMATH Open document ID: 0822.76098
author: Mohammad Rammaha
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-02-09T00:00:00Z
review text: We consider the motion of a compressible perfectly conducting fluid in a magnetic field described by the Lundquist equations. We present two results on the formation of singularities in smooth magnetohydrodynamic waves. The results show that \(C^ 1\)-solutions do not exist in the large under some restrictions on the initial data. The first result is an outcome of ``large'' initial disturbances in three space dimensions. It simply states that the finite-time formation of singularities in three- dimensional magnetohydrodynamic waves is essentially inevitable provided that the initial flow velocity, in some region near the origin, is supersonic relative to the sound speed at infinity. The second result is a ``small'' data result in one space dimension.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 720411
zbMATH Keywords: compressible perfectly conducting fluid
zbMATH Keywords: Lundquist equations
zbMATH Keywords: initial disturbances
zbMATH Keywords: finite-time formation of singularities
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1472
OpenAlex ID: W2027175289
DOI: 10.1006/JMAA.1994.1472
description: scientific article; zbMATH DE number 720411