  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.
