The Brinkman equations for steady flow of an incompressible fluid through rigid porous solid are:
$-\dfrac{\mu_0}{k}\mathbf{v} - \mathrm{grad}p + \mu_0 \Delta \mathbf{v} =0$ and $\mathrm{div}(\mathbf{v}) = 0$ in $\Omega$
where $k > 0$ is the permeability of the solid, $\mu_0 >0$ is the viscosity of the fluid, and $p,\mathbf{v}$ are the pressure and velocity fields.
Suppose that the domain is divided into two disjoint regions and $k$ assumes the values $k_0$ and $k_1$ on them.
My question: Is there a jump condition for this problem due to the discontinuity of $k$ ?
Ans: $\mathrm{jump}(\mathbf{t_n})=0$ where $\mathbf{t_n} := -p\mathbf{n} + \mu_0\nabla \mathbf{v}\;\mathbf{n}$