Stability of a boundary permeation model for Navier-Stokes fluids

Abstract

The stability of a boundary permeation model for incompressible second grade fluids was formulated and solved for bounded regions, by Maritz and Sauer. Under an additional boundary condition they proved exponential decay to the rest state provided the initial energy of the system is not too large. In this exposition, we apply the same model to the boundary permeation problem, but for incompressible first grade fluids, also known as Navier-Stokes fluids. In our situation, the additional boundary condition is not necessary, but in contrast to the second grade fluid, the decay of perturbed solutions is first order polynomial.