We study the three-dimensional compressible elastic Navier-Stokes-Poisson equations, which model the motion of a kind of compressible electrically conducting viscoelastic flows. In the Poisson equation, the positive background charge satisfies the constant distribution or the Boltzmann distribution. Under the Hodge boundary condition for the velocity and the Dirichlet or Neumann boundary condition for the electrostatic potential, we obtain the uniquely global strong solution near a constant equilibrium state for the half-space problem by a delicate energy method.
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