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arXiv · 1606.05038

Zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions

Fucai Li·Zhipeng Zhang
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Abstract

We investigate the zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. We obtain the uniform regularity of solutions with respect to the kinematic viscosity coefficient and the magnetic diffusivity coefficient. These solutions are uniformly bounded in a conormal Sobolev space and $W^{1,\infty}(\Omega)$ which allow us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence.

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Fucai Li, Zhipeng Zhang. 2016-06-16. Zero kinematic viscosity-magnetic diffusion limit of the incompressible viscous magnetohydrodynamic equations with Navier boundary conditions. https://arxiv.org/abs/1606.05038

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