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A Regularity Criterion for the Density-Dependent Magnetohydrodynamics System in Critical Besov Spaces

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Abstract

In this paper, we study the Cauchy problem for incompressible density-dependent magnetohydrodynamics system in \(\mathbb R^N\ (N \ge 2)\). We prove the regularity criterion of solutions in the critical Besov spaces. For the proof of the results we use the commutator estimate and product estimate for nonlinear term.

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Acknowledgements

The author would like to express gratitude to Professor Takayoshi Ogawa for his many helpful suggestions. He is also greateful to Professor Hideo Kozono for his valuable advices. Finaly, he really thank referees for their comments, which led to improvements in the presentation of this paper.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Ryosuke Nakasato

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  1. Ryosuke Nakasato
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Correspondence to Ryosuke Nakasato.

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Communicated by Y. Giga.

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Nakasato, R. A Regularity Criterion for the Density-Dependent Magnetohydrodynamics System in Critical Besov Spaces. J. Math. Fluid Mech. 20, 1911–1919 (2018). https://doi.org/10.1007/s00021-018-0393-2

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  • DOI: https://doi.org/10.1007/s00021-018-0393-2

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