Global existence and large time behavior of solutions for compressible quantum magnetohydrodynamics flows in T3

The present paper concerns with compressible quantum magnetohydrodynamic flows in T3. This new model was derived by Haas [13] from a Wigner-Maxwell system. First, we reformulate this system as the quantum Euler-Maxwell system by using effective velocity. Then, the global existence of weak solutions is obtained by adding artificial viscosity terms and the Faedo-Galerkin method together with weak compactness techniques. Moreover, large time behavior of solutions is established.