Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions (Advances in Applied Mathematics and Mechanics, 2021)
In this paper we prove first the existence and uniqueness results for the weak solution, to thestationary equations for Bingham fluid in a three dimensional bounded domainwith Fourier and Tresca boundary condition; then we study the asymptoticanalysis when one dimension of the fluid domain tends to zero. The strongconvergence of the velocity is proved, and a specific Reynolds limit equationand the limit of Tresca free boundary conditions are obtained.