Existence of Global Strong Solutions to a Beam–Fluid Interaction System
Reads0
Chats0
TLDR
In this paper, the authors considered an unsteady nonlinear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoelastic arteries and proved that strong solutions to this problem are global-in-time.Abstract:
We study an unsteady nonlinear fluid–structure interaction problem which is a simplified model to describe blood flow through viscoelastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid–structure interface and the action–reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain, in particular that contact between the viscoelastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, and of the existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure.read more
Citations
More filters
Journal ArticleDOI
A Nitsche-based formulation for fluid-structure interactions with contact
TL;DR: In this paper, the authors derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact, based on the work of Chouly and Hild.
Journal ArticleDOI
Existence of local strong solutions to fluid-beam and fluid-rod interaction systems
TL;DR: In this paper, the authors consider an unsteady nonlinear fluid-structure interaction problem and prove existence of a unique local-in-time strong solution for which no viscosity is added.
Journal ArticleDOI
Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure
TL;DR: In this paper, the authors consider a system modeling the interaction between a viscous incompressible fluid and an elastic structure, where the fluid motion is represented by the classical Navier-Stokes equations while the elastic displacement is described by the linearized elasticity equation.
Posted Content
Existence and regularity for weak solutions for a fluid interacting with a non-linear shell in 3D
TL;DR: In this paper, a-priori estimates that reveal higher regularity of the shell displacement beyond energy estimates are obtained by introducing new analytical tools that allow to exploit dissipative effects of the fluid for the (non-dissipative) solid.
Journal ArticleDOI
Maximal-in-time existence and uniqueness of strong solution of a 3d fluid-structure interaction model
TL;DR: This work proves the existence of a unique maximal strong solution of the Navier-Stokes equations in a cylindrical type domain with an elastic structure, governed by a damped shell equation, located at the lateral boundary of the domain occupied by the fluid.
References
More filters
Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
Book
An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems
TL;DR: Steady-State Solutions of the Navier-Stokes Equations: Statement of the Problem and Open Questions as mentioned in this paper The Navier Stokes Equation (NSE) is a stable state solution of the NSE.
MonographDOI
Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes
TL;DR: Advanced Transport Phenomena as mentioned in this paper provides a detailed discussion of modern analytic methods for the solution of fluid mechanics and heat and mass transfer problems focusing on approximations based on scaling and asymptotic methods, beginning with the derivation of basic equations and boundary conditions and concluding with linear stability theory.
Journal ArticleDOI
On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels
TL;DR: In this article, the authors propose an approach to couple the original 3D equations with a convenient 1D model for the analysis of flows in compliant vessels, which allows for a dramatic reduction of the computational complexity and is suitable for ''absorbing» outgoing pressure waves.
Book
Advanced transport phenomena
TL;DR: This book aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
Related Papers (5)
Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell
Daniel Lengeler,Michael Růžička +1 more