Speaker
Description
Motivated by the problem of rigorously justifying reduced elastohydrodynamic models, which are commonly used in microfluidics, we study a fluid–plate interaction system and identify conditions guaranteeing uniform separation of the elastic plate from the opposing rigid boundary.
More precisely, we consider a three-dimensional incompressible viscous fluid governed by the Navier–Stokes equations beneath an elastic plate governed by a fourth-order equation, possibly with square-root structural damping. The two subsystems are coupled through velocity- and stress-matching conditions. We present two sufficient conditions that exclude contact between the plate and the rigid boundary. First, sufficiently small initial kinetic and elastic energies relative to the square of the conserved mean fluid height guarantee a uniform positive lower bound on the plate height and, consequently, global-in-time existence of weak solutions [1]. Second, natural energy bounds together with suitable additional regularity of weak solutions yield uniform control of the reciprocal plate height, without any smallness assumption and even in the absence of structural damping [2].
These results remove a key obstacle to applying rigorous lubrication-approximation techniques used to justify sixth-order thin-film equations as reduced elastohydrodynamic models.
This is joint work with Igor Kukavica (University of Southern California), Linfeng Li (University of California Los Angeles), and Boris Muha (University of Zagreb).
References:
[1] M. Bukal, I. Kukavica, L. Li, and B. Muha. A global existence result on weak solutions for the 3D Navier–Stokes–plate system with no contact. J. Nonlinear Sci. 36, 60 (2026).
[2] M. Bukal, I. Kukavica, L. Li, and B. Muha. A no-contact result for a plate–fluid interaction system in dimension three. To appear in SIAM J. Math. Anal. (2026).