Non‐Newtonian flow in a thin film with boundary conditions of Coulomb's type
Fethi Saidi · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2006
Abstract This paper concerns the asymptotic behavior of solutions of the three‐dimensional non‐Newtonian fluid flow with slip condition of Coulomb's type imposed on a part of the boundary domain. Existence and uniqueness results for the weak solution are proved. We study the limit when the thickness tends to zero and we prove a convergence theorem for velocity and pressure in appropriate functional spaces. The limit of slip condition is obtained. Besides, the uniqueness of the velocity and the pressure limits are also proved.