Decay rates of the compressible viscoelastic flows with electric potential

We study the global existence and decay rates of strong solutions to the three dimensional compressible viscoelastic flows with an electric potential. The energy method for high frequency parts combined with a spectral analysis for low frequency parts is used to obtain the global solution and its decay rate (in time). We show that the density of the solution converges to its equilibrium state at the L2-decay rate (1+t)−34−12 when the initial perturbation admits some small assumptions. Compared to the compressible viscoelastic flows Hu and Wu (2013) [13], our results imply that the rotating effect of the electric field affects the dispersion of fluids and enhances the time decay rate of the density.