Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A uniform estimate for the incompressible magneto-hydrodynamics equations with a slip boundary condition


Authors: Y. Meng and Y.-G. Wang
Journal: Quart. Appl. Math. 74 (2016), 27-48
MSC (2010): Primary 35M13, 35Q35, 76D10, 76D03, 76N20
Published electronically: December 3, 2015
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Abstract: In this paper, we derive a uniform estimate of the strong solution to the incompressible magneto-hydrodynamic (MHD) system with a slip boundary condition in a conormal Sobolev space with viscosity weight. As a consequence of this uniform estimate, we obtain that the solution of the viscous MHD system converges strongly to a solution of the ideal MHD system from a compactness argument.


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Additional Information

Y. Meng
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China — and — School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu, 212003, People’s Republic of China
Email: myp_just@163.com

Y.-G. Wang
Affiliation: Department of Mathematics, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China
Email: ygwang@sjtu.edu.cn

DOI: https://doi.org/10.1090/qam/1406
Keywords: Incompressible MHD equations, uniform estimate, conormal Sobolev spaces, small viscosity limit.
Received by editor(s): March 29, 2014
Published electronically: December 3, 2015
Additional Notes: The first author was supported by the Shanghai Jiao Tong University Innovation Fund for Postgraduates and Scientific Research Fund of Jiangsu University of Science and Technology
This work was partially supported by NNSF of China under the grants 10971134, 11031001, 91230102, and by Shanghai Committee of Science and Technology under the grant 15XD1502300
Article copyright: © Copyright 2015 Brown University


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