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Zero Kinematic Viscosity-Magnetic Diffusion Limit of the Incompressible Viscous Magnetohydrodynamic Equations with Navier Boundary Conditions

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Abstract

We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω ⊂ ℝ3. It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient. The solution is uniformly bounded in a conormal Sobolev space and W1,∞ (Ω) which allows us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence in L∞(0, T; L2), L∞(0, T; W1, p) (2 ≤ p < ∞), and L∞((0, T) × Ω) for some T > 0.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Fucai Li  (栗付才) & Zhipeng Zhang  (张志朋)

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Zhipeng Zhang  (张志朋)

Authors
  1. Fucai Li  (栗付才)
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  2. Zhipeng Zhang  (张志朋)
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Correspondence to Zhipeng Zhang  (张志朋).

Additional information

Li was supported partially by NSFC (11671193, 11971234) and PAPD. Zhang was supported partially by the China Postdoctoral Science Foundation (2019M650581).

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Li, F., Zhang, Z. Zero Kinematic Viscosity-Magnetic Diffusion Limit of the Incompressible Viscous Magnetohydrodynamic Equations with Navier Boundary Conditions. Acta Math Sci 41, 1503–1536 (2021). https://doi.org/10.1007/s10473-021-0507-4

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  • DOI: https://doi.org/10.1007/s10473-021-0507-4

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