Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

Abstract

In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.