On the Domain Dependence of Solutions to the Compressible Navier-Stokes Equations of an Isothermal Fluid

The aim of this paper is to study the behaviour of the variational solutions to the Navier-Stokes equations describing viscous compressible isothermal fluids with nonlinear stress tensors in a sequence of domains ${varOmega_{n}} _{n=1}^{infty}$ . The sequence converges in sense of the Sobolev-Orlicz capacity to domain Ω. We prove that the solutions of the equations in Ω _n converge to a solution of the respective equations in Ω. Moreover, The result can be applied to generalization of the existence result.