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

Authors
  • Li, Fucai1
  • Zhang, Zhipeng1, 2
  • 1 Nanjing University, Nanjing, 210093, China , Nanjing (China)
  • 2 Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China , Beijing (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 29, 2021
Volume
41
Issue
5
Pages
1503–1536
Identifiers
DOI: 10.1007/s10473-021-0507-4
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

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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