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On Some Recent Results from the Theory of MHD Equations

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Fluids Under Control

Part of the book series: Advances in Mathematical Fluid Mechanics ((LNMFM))

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Abstract

This chapter shows the main ideas of the derivation of the MHD and Hall–MHD equations (Sect. 1) and provides a brief survey of qualitative properties of these equations (Sect. 2). Some results that concern the role of the pressure in the theory of the MHD equations are presented in Sect. 3, and one local regularity criterion for suitable weak solutions to the MHD equations, which uses the behavior of the L3-norm of the velocity and the magnetic field as t approaches the hypothetic singular time t0, is presented in Sect. 4.

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Acknowledgements

The first author has been supported by the Grant Agency of the Czech Republic (grant No. 22-08633J) and by the Academy of Sciences of the Czech Republic (RVO 67985840). The second author has been supported by the National Research Foundation of Korea (NRF) grants funded by the Korean government(MSIT) No. 2021R1A2C4002840 and No. 2021K2A9A1A06091213.

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Authors and Affiliations

  1. Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic

    Jiří Neustupa

  2. Department of Mathematics, Yonsei University, Seoul, Republic of Korea

    Minsuk Yang

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  1. Jiří Neustupa
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Correspondence to Jiří Neustupa .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Czech Technical University in Prague, Prague, Czech Republic

    Tomáš Bodnár

  2. Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Giovanni P. Galdi

  3. Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic

    Šárka Nečasová

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Neustupa, J., Yang, M. (2023). On Some Recent Results from the Theory of MHD Equations. In: Bodnár, T., Galdi, G.P., Nečasová, Š. (eds) Fluids Under Control. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-27625-5_6

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