A review on rigorous derivation of reduced models for fluid-structure interaction systems

Abstract

In this paper we review and systematize the mathematical theory on justification of sixth-order thin-film equations as reduced models for various fluid-structure interaction systems in which fluids are lubricating underneath elastic structures. Justification is based on careful examination of energy estimates, weak convergence results of solutions of the original fluid-structure interaction systems to the solution of the sixth-order thin-film equation, and quantitative error estimates which provide even strong convergence results.