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

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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].

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, the Chinese Academy of Sciences, Bei**g, 100080, China

    Zhi-fei Zhang

  2. Department of Mathematics, East China Normal University, Shanghai, 200062, China

    **ao-feng Liu

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  1. Zhi-fei Zhang
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  2. **ao-feng Liu
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Correspondence to Zhi-fei Zhang.

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Zhang, Zf., Liu, Xf. On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations. Acta Mathematicae Applicatae Sinica, English Series 20, 695–700 (2004). https://doi.org/10.1007/s10255-004-0207-6

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  • DOI: https://doi.org/10.1007/s10255-004-0207-6

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