Space-time decay rate for strong solutions to the viscous liquid-gas two-phase flow with magnetic field

We investigate the viscous liquid -gas two-phase model with magnetic field in a weighted Sobolev space Ha2(R3). Based on precise weighted energy estimation, we establish the space-time decay rates of the k(is an element of [0, 2])th order spatial derivative of strong solutions. The main difficulty comes from the lack of dissipative structure of parallel to backward difference P parallel to 2L2 a we need to construct an interactive weighted energy functional to solve it. , and