Justification of a nonlinear sixth-order thin-film equation as the reduced model for a fluid–structure interaction problem

Starting from a nonlinear 2D/1D fluid-structure interaction problem between thin layer of viscous fluid and elastic structure, on the vanishing limit relative thickness, we rigorously derive sixth-order thin-film equation describing dynamics vertical displacements structure. The procedure is essentially based quantitative energy estimates, quantified in terms uniform no-contact result structure solid substrate. justified sense strong convergence rescaled to unique positive classical solution equation. Moreover, velocity pressure can be expressed solely