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Open Access Research

A single exponential BKM type estimate for the 3D incompressible ideal MHD equations

Jianli Liu1, Fenglun Wei1 and Kejia Pan23*

Author Affiliations

1 Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China

2 School of Mathematics and Statistics, Central South University, Changsha, 410083, P.R. China

3 Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Central South University, Changsha, 410083, P.R. China

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Boundary Value Problems 2014, 2014:96  doi:10.1186/1687-2770-2014-96

Published: 6 May 2014

Abstract

In this paper, we give a Beale-Kato-Majda type criterion of strong solutions to the incompressible ideal MHD equations. Instead of double exponential estimates, we get a single exponential bound on <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/96/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/96/mathml/M1">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/96/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/96/mathml/M2">View MathML</a>). It can be applied to a system of an ideal viscoelastic flow.

MSC: 35B65, 76W05.

Keywords:
MHD equations; ideal viscoelastic flow; Beale-Kato-Majda criterion; single exponential bound