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The Global Solvability of 3-D Inhomogeneous Viscous Incompressible Magnetohydrodynamic Equations with Bounded Density

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Abstract

The present paper deals with the Cauchy problem of the inhomogeneous viscous incompressible magnetohydrodynamic equations in \({\mathbb {R}}^{3}\). We first prove the global solvability of the model in critical regularity framework with respect to the scaling of the associated equations when initial density is bounded from above and below by some positive constants and initial velocity and magnetic are sufficiently small. Using the same idea, we also obtain the global existence of solutions to the model without any smallness condition imposed on the third component of the initial velocity field and magnetic field in critical Besov spaces and present a lower bound for the lifespan of smooth solutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, Shandong, China

    Fuyi Xu & Liening Qiao

  2. School of Agricultural Engineering and Food Science, Shandong University of Technology, Zibo, 255049, Shandong, China

    Liening Qiao & Peng Fu

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  1. Fuyi Xu
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  2. Liening Qiao
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  3. Peng Fu
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Correspondence to Fuyi Xu or Peng Fu.

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Communicated by G. P. Galdi.

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Research supported by the National Natural Science Foundation of China (11501332, 11771043, 51976112), the Natural Science Foundation of Shandong Province (ZR2015AL007), and Young Scholars Research Fund of Shandong University of Technology.

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Xu, F., Qiao, L. & Fu, P. The Global Solvability of 3-D Inhomogeneous Viscous Incompressible Magnetohydrodynamic Equations with Bounded Density. J. Math. Fluid Mech. 24, 4 (2022). https://doi.org/10.1007/s00021-021-00632-9

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