The interaction between quasilinear elastodynamics and the Navier-Stokes equations

DOI10.1007/s00205-005-0385-2zbMath1138.74325arXivmath/0503431OpenAlexW2089060615MaRDI QIDQ818542

Steve Shkoller, Daniel Coutand

Publication date: 21 March 2006

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503431

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Navier-Stokes equations (35Q30) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25)

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Cites Work

• Unnamed Item
• Unnamed Item
• Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate
• Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
• Existence pour un problème de l'élastodynamique Neumann non linéaire en dimension 2. (Existence for an elasto-dynamic nonlinear Neumann problem in two dimensions)
• An existence theorem for the Dirichlet problem in the elastodynamics of incompressible materials
• Deformations of incompressible bodies with free boundaries
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Existence of weak solutions for the motion of rigid bodies in a viscous fluid
• Chute stationnaire d'un solide dans un fluide visqueux incompressible le long d'un plan incliné. (Free steady fall of a solid in a fluid, along a ramp).
• Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions
• Fluid-structure interaction: Analysis of a 3-D compressible model
• Motion of an elastic solid inside an incompressible viscous fluid
• Chute libre d’un solide dans un fluide visqueux incompressible. existence
• Existence et unicité de solutions d'un problème de couplage fluide-structure bidimensionnel stationnaire
• Existence of solutions for the equations
• Existence for an Unsteady Fluid-Structure Interaction Problem
• Variational properties of steady fall in Stokes flow
• An Eulerian description of fluids containing viscoelastic particles
• Weak solutions for a fluid-elastic structure interaction model