We obtain, via a Galerkin argument, the existence of a unique weak solution to the initial-boundary value problem for an incompressible bipolar viscous fluid satisfying nonhomogeneous boundary conditions. The analysis depends on the derivation of several key a priori estimates. Regularity results are also established and the solution is proven to be asymptotically stable when the forcing function and initial and boundary data decay in an appropriate sense.
"Existence, uniqueness, and stability of solutions to the initial-boundary value problem for bipolar viscous fluids." Differential Integral Equations 8 (2) 453 - 464, 1995.