Variational methods for fluid-structure interaction and porous media

2021/01/23 by B. Benesova, Benesova, B., M. Kampschulte +3 · 1 citation
Computer Science · Engineering · #35Q35 #35Q74 #74F10 (Primary) 35Q30 #74H20 #76D03 #76S05 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2101.09578

openalex publication_date 2021/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• A novel approach to study the wellposedness of the 3D fluid-2D plate interaction PDE System

Related

• A variational approach to hyperbolic evolutions and fluid-structure interactions
• Fluid-poroviscoelastic structure interaction problem with nonlinear geometric coupling
• Variational methods for steady-state Darcy/Fick flow in swollen and\n poroelastic solids
• Weak Solutions in Nonlinear Poroelasticity with Incompressible Constituents
• Variational geometric approach to the thermodynamics of porous media