A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact
Analysis of PDEs
2025-12-12 v2
Abstract
We consider the three-dimensional fluid-structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible Navier-Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. We show that under a rather general condition on the initial data, there exists a global-in-time weak solution of the system. In particular, there is no contact between the plate and the bottom boundary.
Keywords
Cite
@article{arxiv.2511.22754,
title = {A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact},
author = {Mario Bukal and Igor Kukavica and Linfeng Li and Boris Muha},
journal= {arXiv preprint arXiv:2511.22754},
year = {2025}
}