Acta Mathematicae Applicatae Sinica

, Volume 20, Issue 4, pp 695–700

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

Original Papers

DOI: 10.1007/s10255-004-0207-6

Cite this article as:
Zhang, Z. & Liu, X. Acta Mathematicae Applicatae Sinica, English Series (2004) 20: 695. doi:10.1007/s10255-004-0207-6


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].


Ideal MHD equations blow-up littlewood-paley decomposition besov space 

2000 MR Subject Classification

76W05 35B65 

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Academy of Mathematics and Systems Sciencethe Chinese Academy of SciencesBeijingChina
  2. 2.Department of MathematicsEast China Normal UniversityShanghaiChina

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