Global strong solutions of the density-dependent incompressible MHD system with zero resistivity in a bounded domain
Abstract
In this paper, we first establish a regularity criterion for the strong solutions to the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Then we use it and the bootstrap argument to prove the global well-posedness provided that the initial data u0 and b0 satisfy that (d-2)||∇u0 || L2+||b0||w1,p are sufficiently small with 
. We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.
Keyword : MHD, zero resistivity, bounded domain
How to Cite
Fan, J., Samet, B., & Zhou, Y. (2019). Global strong solutions of the density-dependent incompressible MHD system with zero resistivity in a bounded domain. Mathematical Modelling and Analysis, 24(1), 95-104. https://doi.org/10.3846/mma.2019.007
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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[11] H. Wu. Strong solution to the incompressible magnetohydrodynamic equations with vacuum. Comput. Math. Appl., 61(9):2742–2753, 2011. https://doi.org/10.1016/j.camwa.2011.03.033 .
[12] J. Wu, X. Xu, Q. Jiu, D. Niu and H. Yu. The 2D magnetohydrodynamic equations with magnetic diffusion. Nonlinearity, 78(11):3935–3955, 2015.