Variational methods for fluid–structure interaction and porous media. (June 2023)

• Record Type: Journal Article
• Authors: Benešová, B.; Kampschulte, M.; Schwarzacher, S.
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Mathematics for continuum mechanics -- Fluid poroelastic structure interactions -- Minimizing movements -- Navier–Stokes equations -- Elastic solids; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103819
• Languages: English
• ISSNs: 1468-1218

Abstract

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 Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms.