This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.
In this paper, we investigate the three-dimensional Cauchy problem of the compressible quantum magnetohydrodynamic model. It is proved that the system admits a unique global solution, provided that the initial energy is suitably small. Furthermore, the large time behavior of the global solution is obtained.
In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows. We prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large oscillations and the initial density may allowed to contain the interior and far field vacuum states. Furthermore, the large time behavior of the solution is obtained as well.
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