On the existence of \(L^{p}\) solutions of the magnetohydrodynamic equations in a bounded domain
type: Item
instance of: scholarly article
title: On the existence of \(L^{p}\) solutions of the magnetohydrodynamic equations in a bounded domain
zbMATH Open document ID: 1025.35021
DOI: 10.1016/S0362-546X(03)00132-9
author: Takahiro Akiyama
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-08-13T00:00:00Z
review text: The aim of this paper is to show the global existence of the nonstationary magnetohydrodynamic equations in \(L^{3}\) for \(L^{3}\) initial data in the vicinity of the trivial solutions without any regularity assumptions on the initial data and study the asymptotic behaviour when \(t\) tends to infinity. The considered domain is supposed to be bounded in \(\mathbb{R}^{3}\) having also as boundary a sufficiently smooth compact hypersurface while the non-slip boundary condition is accomplished with the fulfillment of the perfect conducting wall condition by the magnetic field vector.
reviewed by: Titus Petrila
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1963684
zbMATH Keywords: magnetohydrodynamic equations
zbMATH Keywords: global solutions
zbMATH Keywords: parabolic type Maxwell equations
MaRDI profile type: Publication
cites work: On a Resolvent Estimate of a System of Laplace Operators with Perfect Wall Condition
cites work: Q3255277
cites work: Q4292463
cites work: Q3732186
cites work: Über ein Rand-Anfangswertproblem der Magnetohydrodynamik
cites work: Some mathematical questions related to the mhd equations
description: scientific article; zbMATH DE number 1963684