Global well-posedness of the compressible quantum magnetohydrodynamic model with small initial energy

Abstract

Abstract 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.

Keywords

• Compressible quantum
• Magnetohydrodynamic model
• Small initial energy
• Global existence