The initial boundary value problem for the equations of ideal magneto- hydrodynamics
type: Item
instance of: scholarly article
title: The initial boundary value problem for the equations of ideal magneto- hydrodynamics
zbMATH Open document ID: 0657.76085
author: Taku Yanagisawa
published in: Hokkaido Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: The author proves a local in time existence and uniqueness theorem for the initial boundary value problem of the equations of ideal magnetohydrodynamics over a bounded domain \(\Omega \subset R^ 3\) with \(C^{\infty}\) boundary \(\Gamma\). The initial pressure and magnetic field are chosen such that the equations form a quasilinear symmetric hyperbolic system. Defining appropriate function spaces, the theorem is proved via iteration scheme. At first, the equations are modified to make the boundary noncharacteristic. Secondly, making use of the special structure of the modified equations and the rank of the boundary matrix, it is shown that the limit of the solutions of the modified equations is the solution of the original initial boundary value problem.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4074730
zbMATH Keywords: local in time existence
zbMATH Keywords: uniqueness theorem
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: ideal magnetohydrodynamics
zbMATH Keywords: bounded domain
zbMATH Keywords: initial pressure
zbMATH Keywords: quasilinear symmetric hyperbolic system
zbMATH Keywords: boundary matrix
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381518181
OpenAlex ID: W2043110354
DOI: 10.14492/HOKMJ/1381518181
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description: scientific article; zbMATH DE number 4074730