(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition; then we study the asymptotic analysis when one dimension of the fluid domain tends to zero. The strong convergence of the velocity is proved, and a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.