Steady flow of a Navier-stokes liquid past an elastic body

Giovanni P. Galdi, Mads Kyed

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We perform a mathematical analysis of the steady flow of a viscous liquid, L, past a three-dimensional elastic body, B. We assume that L fills the whole space exterior to B, and that its motion is governed by the Navier-Stokes equations corresponding to non-zero velocity at infinity, v. As for B, we suppose that it is a St. Venant-Kirchhoff material, held in equilibrium either by keeping an interior portion of it attached to a rigid body or by means of appropriate control body force and surface traction. We treat the problem as a coupled steady state fluid-structure problem with the surface of B as a free boundary. Our main goal is to show existence and uniqueness for the coupled system liquid-body, for sufficiently small v This goal is reached by a fixed point approach based upon a suitable reformulation of the Navier-Stokes equation in the reference configuration, along with appropriate a priori estimates of solutions to the corresponding Oseen linearization and to the elasticity equations.

Original languageEnglish
Pages (from-to)849-875
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume194
Issue number3
DOIs
Publication statusPublished - 2009 Oct
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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