On the stationary interaction of a Navier-Stokes fluid with an elastic tube wall

Abstract

We study the stationary problem of a viscous, incompressible Navier-Stokes fluid flowing through a flexible tube with thickness. The behavior of the elastic walls of the tube is described by the equations of nonlinear elasticity for a St.Venant-Kirchhoff material. For smooth enough applied exterior forces we prove the existence of a solution to the coupled problem.

Keywords:

• Fluid-structure interaction;
• Navier-stokes equations
• Existence and regularity of solutions

Keywords:

• 2000 Mathematics Subject Classifications:
• 74F10
• 35Q30
• 76D03

Acknowledgment

The author would like to thank Prof. Willi Jäger for interesting discussions relatively to this work. This work was supported by the DFG in the SFB 359 (University of Heidelberg.)

Notes

¹ is the characteristic function of .