Abstract The Dirichlet problem for the Brinkman system is studied in W^1, q (, {R}ᵐ) Lqₗoc () W 1, q (Ω, R m) × L loc q (Ω ¯) for unbounded domains {R}ᵐ Ω ⊂ R m with compact Lipschitz boundary. If the boundary of Ω is of class {C}^k, 1 C k, 1 we are able to study this problem in W^k+1, q (, {R}ᵐ) D^k, q () W k + 1, q (Ω, R m) × D k, q (Ω). Here W^k, q () W k, q (Ω) denotes Sobolev space and D^k, q () D k, q (Ω) denotes homogeneous Sobolev space. We use the integral equation method. So, we are interested about behavior of volume potentials and also boundary layer potentials. As a consequence of results for the Brinkman system we prove the existence of a solution of the Dirichlet problem for the Darcy–Forchheimer–Brinkman system in the same function spaces.
Dagmar Medková (Thu,) studied this question.