Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model

DOI10.1137/18M1178451zbMath1456.35165OpenAlexW3047068965MaRDI QIDQ5141944

Debayan Maity, Arnab Roy, Jean-Pierre Raymond

Publication date: 29 December 2020

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

Full work available at URL: https://doi.org/10.1137/18m1178451

zbMATH Keywords

strong solutionsincompressible Navier-Stokes systemnonlinear shell modelfluid-structure interaction system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Existence of global strong solutions to a beam-fluid interaction system
• A fluid-structure model coupling the Navier-Stokes equations and the Lamé system
• Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate
• Representation and control of infinite dimensional systems
• Proof of extensions of two conjectures on structural damping for elastic systems
• On the existence of strong solutions to a coupled fluid-structure evolution problem
• Motion of an elastic solid inside an incompressible viscous fluid
• Perturbation theory for linear operators.
• 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
• Fluid-structure system with boundary conditions involving the pressure
• A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof
• Existence of a solution to a fluid-multi-layered-structure interaction problem
• Existence of strong solutions for a system coupling the Navier-Stokes equations and a damped wave equation
• Existence of local strong solutions to fluid-beam and fluid-rod interaction systems
• Weak solutions for an incompressible Newtonian fluid interacting with a Koiter type shell
• Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
• Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain
• A short course on operator semigroups
• Solutions to a Free Boundary Problem of Fluid-Structure Interaction
• Weak Solutions for An Incompressible, Generalized Newtonian Fluid Interacting with a Linearly Elastic Koiter Type Shell
• Fluid–Structure Interaction in Hemodynamics: Modeling, Analysis, and Numerical Simulation
• Boundary Stabilization of the Navier--Stokes Equations in the Case of Mixed Boundary Conditions
• Feedback Stabilization of a Fluid-Structure Model
• Existence of Strong Solutions to a Fluid-Structure System
• Navier–Stokes Equations Interacting with a Nonlinear Elastic Biofluid Shell
• Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate
• Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods.
• Existence for an Unsteady Fluid-Structure Interaction Problem
• Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure
• Feedback Stabilization of a Two-Dimensional Fluid-Structure Interaction System with Mixed Boundary Conditions
• The Interaction of the 3D Navier–Stokes Equations with a Moving Nonlinear Koiter Elastic Shell
• Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy