Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations

Abstract

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 H2 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.

Keywords

• elastic navier-stokes-poisson equations
• initial-boundary value problems
• global solution
• exponential decay
• 76a10
• 35q35
• 35g61