In this paper, we consider a region occupied by viscous or inviscid compressible magnetohydrodynamic fluids and surrounded by vacuum. It is shown that the fluid region will expand at least linearly in time as soon as there are no singularities. The expanding rate is proportional to initial total energy and is inversely proportional to initial mass. The result indicates an interesting fact that the expansion of the viscous monatomic fluids seems similar to that of the inviscid fluids.
We are concerned about the barotropic compressible Navier-Stokes equations with densitydependent viscosities which may degenerate in vacuum. We show that any classical solution to barotropic compressible Navier-Stokes equations in a periodic domain will blow up, when the initial density admits an isolated mass group and the viscousity coefficients satisfy some conditions. A new condition on viscosities is first put forward in this paper.
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