Study Of Stokes Dynamical System In A Thin Domain With Fourier And Tresca Boundary Conditions

Asymptotic analysis of an incompressible Stokes fluid in a dynamic regime in a three-dimensional thin domain Omega? with mixed boundary conditions and Tresca friction law is studied in this paper. The problem statement and variational formulation of the problem are reformulated in a fixed domain. In which case, the estimates on velocity and pressure are proved. These estimates will be useful in order to give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.