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

Autori
Bukal, Mario ; Muha, Boris

Izvornik
Nonlinearity (0951-7715) 35 (2022), 8; 4695-4726

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
thin viscous fluids ; nonlinear fluid-structure interaction ; nonlinear sixth-order thin-film equation

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

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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