Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data

2020 ◽  
Author(s):  
Kunquan Li ◽  
Zilai Li ◽  
Yaobin Ou
Keyword(s):  
Free Boundary ◽  
Initial Data ◽  
Classical Solutions ◽  
Magnetohydrodynamic Equations ◽  
Large Initial Data

On the global solvability of the coupled kinetic-fluid system for flocking with large initial data

2017 ◽  
Vol 28 (01) ◽  
pp. 1-60 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Bingkang Huang ◽  
Qinghua Xiao ◽  
Xiongtao Zhang
Keyword(s):  
Initial Data ◽  
Coupled Model ◽  
Global Solvability ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Degenerate Diffusion ◽  
Large Initial Data ◽  
Fluid System ◽  
Planar Wave

We study the dynamics of infinitely many Cucker–Smale (CS) flocking particles under the interplay of random communication and compressible fluids in planar wave case. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker–Smale–Fokker–Planck (CS–FP) equation with a degenerate diffusion, whereas for the fluid component, we use the compressible Navier–Stokes (NS) equations. These two subsystems are coupled via the drag force. For this coupled model, we present a global existence of classical solutions for arbitrarily large initial data which may contain vacuum.

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