Variational methods for fluid-structure interaction and porous media
Analysis of PDEs
2022-01-12 v2
Abstract
In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Frechet derivative of a non-convex functional as well as (second order in time) inertia terms.
Cite
@article{arxiv.2101.09578,
title = {Variational methods for fluid-structure interaction and porous media},
author = {B. Benesova and M. Kampschulte and S. Schwarzacher},
journal= {arXiv preprint arXiv:2101.09578},
year = {2022}
}
Comments
Revised version with stronger focus on the connections to porous media problems