The Interaction of the 3D Navier–Stokes Equations with a Moving Nonlinear Koiter Elastic Shell

DOI10.1137/080741628zbMath1420.74004OpenAlexW2057189031MaRDI QIDQ5392368

C. H. Arthur Cheng, Steve Shkoller

Publication date: 8 April 2011

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/080741628

zbMATH Keywords

Sobolev spaceexistenceuniquenessmoving boundary value problem

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Shells (74K25) Navier-Stokes equations (35Q30) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (32)

Some Analytical Issues for Elastic Complex Fluids ⋮ A nonlinear fluid-structure interaction problem in compliant arteries treated with vascular stents ⋮ On a fluid–structure interaction problem for plaque growth ⋮ Local well-posedness of free-boundary incompressible elastodynamics with surface tension via vanishing viscosity limit ⋮ Weak-Strong Uniqueness for an Elastic Plate Interacting with the Navier--Stokes Equation ⋮ Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation ⋮ Navier-Stokes-Fourier fluids interacting with elastic shells ⋮ Short-time existence of a quasi-stationary fluid-structure interaction problem for plaque growth ⋮ The Peskin Problem with \({\boldsymbol{\dot B^1_{\infty,\infty }}}\) Initial Data ⋮ An inviscid free boundary fluid-wave model ⋮ The Peskin problem with viscosity contrast ⋮ Well-posedness of solutions to stochastic fluid-structure interaction ⋮ Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls ⋮ Regularity results in 2D fluid-structure interaction ⋮ Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions ⋮ Weak solutions for an incompressible Newtonian fluid interacting with a Koiter type shell ⋮ Analysis of a 3D nonlinear, moving boundary problem describing fluid-mesh-shell interaction ⋮ On the splash singularity for the free-surface of a Navier-Stokes fluid ⋮ A note on the trace theorem for domains which are locally subgraph of a Hölder continuous function ⋮ Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model ⋮ Well-posedness of the free boundary problem for incompressible elastodynamics ⋮ Moving boundary problems ⋮ Stability of the Stokes immersed boundary problem with bending and stretching energy ⋮ Compressible fluids interacting with a linear-elastic shell ⋮ Zero surface tension limit of viscous surface waves ⋮ On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem ⋮ The Viscous Surface Wave Problem with Generalized Surface Energies ⋮ A stochastically perturbed fluid-structure interaction problem modeled by a stochastic viscous wave equation ⋮ Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation^* ⋮ A partitioned numerical scheme for fluid–structure interaction with slip ⋮ Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction ⋮ On a fluid-structure interaction problem for plaque growth: cylindrical domain

This page was built for publication: The Interaction of the 3D Navier–Stokes Equations with a Moving Nonlinear Koiter Elastic Shell