Global-in-time solutions to three-dimensional magnetohydrodynamics equations with a class of large initial data

2019 ◽  
Vol 156 (1) ◽  
pp. 69-90
Author(s):  
Xiaoxin Zheng ◽  
Xiang Bai
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Large Initial Data ◽  
Magnetohydrodynamics Equations

The convergence rate of the fast signal diffusion limit for a Keller–Segel–Stokes system with large initial data

2020 ◽  
pp. 1-41
Author(s):  
Min Li ◽  
Zhaoyin Xiang
Keyword(s):  
Initial Data ◽  
Convergence Rate ◽  
Stokes System ◽  
Smooth Boundary ◽  
Three Dimensional ◽  
Diffusion Limit ◽  
Large Initial Data ◽  
Volume Filling ◽  
Algebraic Convergence ◽  
Current Setting

In this paper, we investigate the fast signal diffusion limit of solutions of the fully parabolic Keller–Segel–Stokes system to solution of the parabolic–elliptic-fluid counterpart in a two-dimensional or three-dimensional bounded domain with smooth boundary. Under the natural volume-filling assumption, we establish an algebraic convergence rate of the fast signal diffusion limit for general large initial data by developing a series of subtle bootstrap arguments for combinational functionals and using some maximal regularities. In our current setting, in particular, we can remove the restriction to asserting convergence only along some subsequence in Wang–Winkler and the second author (Cal. Var., 2019).

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