Asymptotic analysis of a non-Newtonian fluid in a thin domain with Tresca law Original Research Article

In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for non-Newtonian and incompressible fluid in a three-dimensional bounded domain with Tresca fluid–solid interface on one part of the boundary and Dirichlet one on the other part; then we study the asymptotic analysis when one dimension of the fluid domain tend to zero. The strong convergence of the velocity is proved, a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained. The uniqueness of the velocity limit and the pressure limit are also proved.