TY - JOUR

T1 - Steady flow of a Navier-stokes liquid past an elastic body

AU - Galdi, Giovanni P.

AU - Kyed, Mads

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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.

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U2 - 10.1007/s00205-009-0224-y

DO - 10.1007/s00205-009-0224-y

M3 - Article

AN - SCOPUS:70449133691

SN - 0003-9527

VL - 194

SP - 849

EP - 875

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -