Global well-posedness of the compressible electrically conducting viscoelastic fluids subject to the Coulomb force in the half space

Abstract

We study the compressible elastic Navier-Stokes-Poisson equations in the three-dimensional upper half space, which describe the dynamics of some kind of compressible electrically conducting viscoelastic fluids subject to the Coulomb force. Under the Hodge boundary condition for the velocity and the Neumann boundary condition for the electrostatic potential, we obtain the unique global solution near a constant equilibrium state in $H^2$ space by a delicate energy method. To capture the loss of boundary information for the deformation gradient, we propose the Hodge boundary condition for the deformation which can be preserved over time. Moreover, we use the effective electric field instead of the original one which is proved to have a regularization effect for unbounded problems.