Non-isothermal lubrication problem with Tresca fluid–solid interface law. Part II Asymptotic behavior of weak solutions

We study in this paper the asymptotic analysis of an incompressible Newtonian and non-isothermal problem, when one dimension of the fluid domain tends to zero. We prove the strong convergence of the unknowns which are the temperature, the velocity and the pressure of the fluid, we obtain the limit problem with the specific Reynolds equation, and we also prove the uniqueness of the limit temperature velocity and pressure distributions.