We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.

中文翻译：

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三维可压缩弹性纳维-斯托克斯-泊松方程的初边值问题

我们研究了静电势的 Dirichlet 或 Neumann 边界条件下三维可压缩弹性 Navier-Stokes-Poisson 方程的初边界值问题。获得了H 2 空间中恒定平衡态附近的唯一全局解。此外，我们证明了随着时间趋于无穷大，解以指数速率衰减到平衡状态。这是在静电势的各种边界条件下三维弹性纳维-斯托克斯-泊松方程的第一个结果。