An approximation of the axially symmetric flow through a pipe-like domain with a moving part of a boundary
Ján Filo, Volker Pluschke · Boundary Value Problems · 2013
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.