The aim of our work is to give a well-posedness result for a boundary value
problem of transmission-type for the nonlinear, generalized
Darcy-Forchheimer-Brinkman and Stokes systems in complementary Lipschitz
domains in R3. First, we introduce the Sobolev spaces in which we seek our
solution, then we define the trace operators and conormal derivative
operators that are involved in the boundary conditions of our treated
problem. Next, we state a result that concerns the well-posedness of the
transmission problem for the generalized Brinkman and Stokes system in
complementary Lipschitz domains in R3. Afterwards, we state and prove an
important lemma. Finally, we obtain our desired result by employing the
well-posedness of the linearized version of our problem and Banach?s fixed
point theorem.
Local well-posedness of a dispersive Navier-Stokes system
