L-2-Decay of Solutions to the Navier-Stokes System with Navier-Type Boundary Conditions

We study in this paper the L-2-decay to the solutions of the Navier-Stokes system with Navier-type boundary conditions in a domain Omega not necessarily simply connected. Since under this condition the Stokes operator has a non-trivial kernel we consider the solution lying in the orthogonal of that kernel. We also compare the decay rate of a weak solution to the Navier-Stokes problem with the solution to the linear problem emanating from the same initial data.