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A mixed variational formulation of some problems in $L^2$-based Sobolevspaces is used to define the Newtonian and layer potentials for the Stokessystem with $L^{\infty}$ coefficients on Lipschitz domains in ${\mathbb R}^3$.Then the solution of the exterior Dirichlet problem for the Stokes system with$L^{\infty}$ coefficients is presented in terms of these potentials and theinverse of the corresponding single layer operator.

Newtonian and single layer potentials for the Stokes system with $L^{\infty}$ coefficients and the exterior Dirichlet problem