Rigorous derivation of a linear sixth-order thin-film equation as a reduced model for thin fluid-thin structure interaction problems

DOI10.1007/s00245-020-09709-9zbMath1487.35314arXiv1910.00354OpenAlexW3099098544MaRDI QIDQ2232792

Mario Bukal, Boris Muha

Publication date: 8 October 2021

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.00354

zbMATH Keywords

error estimatesfluid-structure interactionelastic platelinear sixth-order thin-film equationthin viscous fluids

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) 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) Thin fluid films (76A20) Lubrication theory (76D08) PDEs in connection with mechanics of deformable solids (35Q74) Mixed-type systems of PDEs (35M30)

Related Items

Justification of a nonlinear sixth-order thin-film equation as the reduced model for a fluid–structure interaction problem ⋮ A review on rigorous derivation of reduced models for fluid-structure interaction systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A modern course in aeroelasticity
• The uniform Korn-Poincaré inequality in thin domains
• Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate
• The interaction between quasilinear elastodynamics and the Navier-Stokes equations
• Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction
• The transition between the Stokes equations and the Reynolds equation: A mathematical proof
• Mathematical theory of evolutionary fluid-flow structure interactions
• Analysis of a linear fluid-structure interaction problem
• Three dimensional asymptotic analysis of an axisymmetric flow in a thin tube with thin stiff elastic wall
• Viscous fluid-thin elastic plate interaction: asymptotic analysis with respect to the rigidity and density of the plate
• A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects
• Existence of a solution to a fluid-multi-layered-structure interaction problem
• Fluid-structure interaction and biomedical applications
• Fluid-structure interaction in a pre-stressed tube with thick elastic walls. I: The stationary Stokes problem
• Asymptotic analysis of a periodic flow in a thin channel with viscoelastic wall
• Dynamics of a nonlinear elastic plate interacting with a linearized compressible viscous fluid
• Fluid Film Lubrication
• Multiple equilibria in a simple elastocapillary system
• The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• The Isolation Oxidation of Silicon: The Reaction-Controlled Case
• Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité
• Elliptic Partial Differential Equations of Second Order
• Effective Equations Modeling the Flow of a Viscous Incompressible Fluid through a Long Elastic Tube Arising in the Study of Blood Flow through Small Arteries
• The Periodic Unfolding Method
• Elastic-plated gravity currents
• Asymptotic analysis of a viscous fluid–thin plate interaction: Periodic flow
• Asymptotic analysis of a thin fluid layer-elastic plate interaction problem
• An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics
• Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip
• ASYMPTOTIC BEHAVIOR OF STRUCTURES MADE OF PLATES
• The effects of flexion and torsion on a fluid flow through a curved pipe