On the well-posedness of generalized Darcy–Forchheimer equation
Johnson Daddy Audu, Faisal A. Fairag, Salim A. Messaoudi · Boundary Value Problems · 2018
Under the necessary compatibility condition and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and stability of solution in $[L^{m+1}(\Omega )]^{d}\times(W^{1, \frac{m+1}{m}}(\Omega)\cap L^{2}_{0}(\Omega))$ for a generalized Darcy–Forchheimer model, governing a non-Darcy flows in porous media with dimension $d=2, 3$ and $m\in(1, 2]$ .