Asymptotic behavior of a steady flow in a two-dimensional pipe

Tom 158 / 2003

Piotr Bogusław Mucha Studia Mathematica 158 (2003), 39-58 MSC: 35B40, 76D05, 35C20, 35Q30. DOI: 10.4064/sm158-1-4


The paper investigates the asymptotic behavior of a steady flow of an incompressible viscous fluid in a two-dimensional infinite pipe with slip boundary conditions and large flux. The convergence of the solutions to data at infinities is examined. The technique enables computing optimal factors of exponential decay at the outlet and inlet of the pipe which are unsymmetric for nonzero fluxes of the flow. As a corollary, the asymptotic structure of the solutions is obtained. The results show strong dependence on the magnitude of the Reynolds number.


  • Piotr Bogusław MuchaInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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