Asymptotic Analysis of a Viscous Flow in a Curved Pipe with Elastic Walls

  • Gonzalo Castiñeira
  • José M. Rodríguez
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 8)


This communication is devoted to the presentation of our recent results regarding the asymptotic analysis of a viscous flow in a tube with elastic walls. This study can be applied, for example, to the blood flow in an artery. With this aim, we consider the dynamic problem of the incompressible flow of a viscous fluid through a curved pipe with a smooth central curve. Our analysis leads to the obtention of an one dimensional model via singular perturbation of the Navier-Stokes system as \(\varepsilon\), a non dimensional parameter related to the radius of cross-section of the tube, tends to zero. We allow the radius depend on tangential direction and time, so a coupling with an elastic or viscoelastic law on the wall of the pipe is possible. To perform the asymptotic analysis, we take a change of variable to a reference domain where we assume the existence of asymptotic expansions on \(\varepsilon\) for both velocity and pressure which, upon substitution on Navier-Stokes equations, leads to the characterization of various terms of the expansion. This allows us to obtain an approximation of the solution of the Navier-Stokes equations.


Asymptotic Expansion Asymptotic Analysis Pipe Wall Transversal Velocity Rigid Wall 
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This research was partially supported by Ministerio de Economía y Competitividad under grant MTM2012-36452-C02-01 with the participation of FEDER.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Facultad de Matemáticas, Departamento de Matemática AplicadaUniv. de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Departamento de Métodos Matemáticos y de Representación, E.T.S. ArquitecturaUniversidade da CoruñaA CoruñaSpain

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