In this study, we continue our study of the Cauchy problem associated with the Brinkman equations see (1.1) and (1.2) below which model fluid flow in certain types of porous media. Here, we will consider the flow in the upper half-space R-+(3) = {(x, y, z) is an element of R-3 vertical bar z >= 0}, under the assumption that the plane z = 0 is impenetrable to the fluid. This means that we will have to introduce boundary conditions that must be attached to the Brinkman equations. We study local and global well-posedness in appropriate Sobolev spaces introduced below, using Kato's theory for quasilinear equations, parabolic regularization and a comparison principle for the solutions of the problem.
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