Regularity issues in the problem of fluid-structure interaction

DOI10.1007/s00205-008-0202-9zbMath1192.35131arXiv0805.2654OpenAlexW2069242947MaRDI QIDQ849233

Matthieu Hillairet, David Gérard-Varet

Publication date: 25 February 2010

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

Full work available at URL: https://arxiv.org/abs/0805.2654

zbMATH Keywords

smooth boundarycollisionfluid-body interaction

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exposant critique de Sobolev et régularité des solutions d'équations elliptiques. (Critical Sobolev exponent and regularity of solutions of elliptic equations)
• Ordinary differential equations, transport theory and Sobolev spaces
• Existence of weak solutions for the motion of rigid bodies in a viscous fluid
• Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid
• On the motion of rigid bodies in a viscous incompressible fluid.
• Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions
• Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
• On a motion of a ball in a viscous fluid.
• Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain
• \(H^p\) spaces of several variables
• Particle–wall collisions in a viscous fluid
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Existence de solutions d'un problème de couplage fluide-structure bidimensionnel instationnaire
• Existence of solutions for the equations
• On Weak Solutions for Fluid‐Rigid Structure Interaction: Compressible and Incompressible Models
• The viscosity of a dilute suspension of rough spheres
• Solid–solid contacts due to surface roughness and their effects on suspension behaviour
• Lack of Collision Between Solid Bodies in a 2D Incompressible Viscous Flow
• A gluey particle model
• LACK OF COLLISION IN A SIMPLIFIED 1D MODEL FOR FLUID–SOLID INTERACTION
• On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere
• The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers
• A slow motion of viscous liquid caused by the rotation of a solid sphere

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