Acta Applicandae Mathematica

, Volume 76, Issue 1, pp 1–15 | Cite as

On Navier–Stokes Equations with Slip Boundary Conditions in an Infinite Pipe

  • Piotr Bogusław Mucha


The paper examines steady Navier–Stokes equations in a two-dimensional infinite pipe with slip boundary conditions. At both inlet and outlet, the velocity of flow is assumed to be constant. The main results show the existence of weak and regular solutions with no restrictions of smallness of the flux vector, also simply connectedness of the domain is not required.

domains with unbounded boundaries steady Navier–Stokes equations slip boundary condition large data 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amick, C. J. and Fraenkel, L. E.: Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types, Acta Math. 144 (1980), 83-152.Google Scholar
  2. 2.
    Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations,Vol. II, Springer-Verlag, New York, 1994.Google Scholar
  3. 3.
    Itoh, S., Tanaka, N. and Tani, A.: The initial value problem for the Navier-Stokes equations with general slip condition, Adv. Math. Sci. Appl. 4 (1994), 51–69.Google Scholar
  4. 4.
    Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1966.Google Scholar
  5. 5.
    Ladyzhenskaya, O. A. and Solonnikov V. A.: Determination of solutions of boundary value problems for steady-state Stokes and Navier-Stokes equations in domains having an unbounded Dirichlet integral, Zap. Nauch. Sem. Len. Ot. Mat. Inst. Steklov (LOMI) 96 (1980), 117–160 (in Russian).Google Scholar
  6. 6.
    Nazarov, S. A. and Pileckas, K. I.: The Reynolds flows of a fluids in a three-dimensional channel, Lit. Mat. Rink. 30 (1990), 772–783 (in Russian).Google Scholar
  7. 7.
    Rivkind, L. P. and Solonnikov, V. A.: On nonsymmetric two-dimensional visous flow through an aparture, Portugal Math. 57(4) (2000), 381–414.Google Scholar
  8. 8.
    Secchi, P.: On a stationary problem for the compressible equations: the self-gravitating eqauilibrium solutions, Differential Integral Equations 7 (1994), 463–482.Google Scholar
  9. 9.
    Solonnikov, V. A. and Scadilov, V. E.: On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov. 125 (1973), 186–199.Google Scholar
  10. 10.
    Temam, R.: Navier-Stokes Equations, North-Holland, Amsterdam, 1977.Google Scholar
  11. 11.
    Zajaczkowski, W. M.: On global special solutions for Navier-Stokes equations with boundary slip conditions in a cylindrical domain, To be published.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Piotr Bogusław Mucha
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsWarsaw UniversityWarsawPoland

Personalised recommendations