An approximation of the axially symmetric flow through a pipe-like domain with a moving part of a boundary

作者：Filo Jan^*; Pluschke Volker

来源：Boundary Value Problems, 2013, 2013(1): 241.

DOI：10.1186/1687-2770-2013-241

• perturbed Navier-Stokes equations
• artificial pressure
• fluid-structure interaction
• cylindrical coordinate system
• Schauder fixed point theorem

The purpose of this work is to study the existence of solutions for approximation of an unsteady fluid-structure interaction problem. We consider a perturbed Navier-Stokes equation in the cylindrical coordinate system assuming axially symmetric flow. A priori unknown part of the boundary (that interacts with the fluid) is governed with a linear equation of fifth order. We prove the existence of at least one weak solution as long as the boundary does not touch the axis of symmetry. An explicit expression for a class of divergence-free functions is given.

• 出版日期2013-11-18