Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data

Mario Bukal; Igor Kukavica; Linfeng Li; Boris Muha

Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data

Analysis of PDEs 2026-07-26 v1

Authors: Mario Bukal , Igor Kukavica , Linfeng Li , Boris Muha

Abstract

We consider a three-dimensional fluid-structure interaction problem coupling the incompressible Navier-Stokes equations in a time-dependent domain with a square-root damped plate equation, which is posed on the moving upper boundary of the fluid. We prove, a priori, the exponential decay of strong solutions for initial data that are sufficiently small in a suitable Sobolev space. The proof combines higher-order energy estimates, Stokes-type regularity bounds, and a nonlinear bootstrap scheme that closes under the smallness assumption.

Keywords

fluid-structure interaction Navier-Stokes equations plate equation exponential decay strong solutions energy estimates

Cite

@article{arxiv.2607.23756,
  title  = {Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data},
  author = {Mario Bukal and Igor Kukavica and Linfeng Li and Boris Muha},
  journal= {arXiv preprint arXiv:2607.23756},
  year   = {2026}
}