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On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations

On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations In this paper, we consider the blow-up of smooth solutions to the 3D ideal MHD equations. Let (u, b) be a smooth solution in (0, T). It is proved that the solution (u, b) can be extended after t = T if $$ {\left( {\nabla \times u,\nabla \times b} \right)} \in L^{1} {\left( {0,T;\ifmmode\expandafter\dot\else\expandafter\.\fi{B}^{0}_{{\infty ,\infty }} } \right)} $$ . This is an improvement of the result given by Caflisch, Klapper, and Steele [3]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-004-0207-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the blow-up of smooth solutions to the 3D ideal MHD equations. Let (u, b) be a smooth solution in (0, T). It is proved that the solution (u, b) can be extended after t = T if $$ {\left( {\nabla \times u,\nabla \times b} \right)} \in L^{1} {\left( {0,T;\ifmmode\expandafter\dot\else\expandafter\.\fi{B}^{0}_{{\infty ,\infty }} } \right)} $$ . This is an improvement of the result given by Caflisch, Klapper, and Steele [3].

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jan 1, 2004

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