A complete general solution of the unsteady Brinkman equations

In this paper, we present a complete general solution of the unsteady Brinkman equations. To this end, we introduce a representation for velocity and pressure in terms of two scalar functions. One of these scalar functions satisfies a second order partial differential equation (PDE) while the other satisfies a fourth order PDE which can be factorized into a pair of second order PDEs. We show that the solution of this fourth order PDE is indeed the sum of the solutions of the two second order PDEs. We also use these solutions to obtain a complete general solution of the unsteady Brinkman equations.