A study of various free boundary value problems in fluid mechanics : The asymptotic behavior of weak solution

Abstract

This thesis investigates the asymptotic behavior of non-isothermal flows of viscoplastic flu-ids (Bingham and Herschel-Bulkley) in thin domains with Tresca-type friction conditions.An effective limit model is derived, combining a Reynolds-type variational inequality with a simplified heat equation. The analysis rigorously proves the existence, uniqueness, and convergence of solutions. These results establish a robust mathematical framework for simulating confined flows, with significant applications in lubrication engineering and pro-cess design.