Abstract
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.
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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.
Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations,Vol. II, Springer-Verlag, New York, 1994.
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.
Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1966.
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).
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).
Rivkind, L. P. and Solonnikov, V. A.: On nonsymmetric two-dimensional visous flow through an aparture, Portugal Math. 57(4) (2000), 381–414.
Secchi, P.: On a stationary problem for the compressible equations: the self-gravitating eqauilibrium solutions, Differential Integral Equations 7 (1994), 463–482.
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.
Temam, R.: Navier-Stokes Equations, North-Holland, Amsterdam, 1977.
Zajaczkowski, W. M.: On global special solutions for Navier-Stokes equations with boundary slip conditions in a cylindrical domain, To be published.
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Mucha, P.B. On Navier–Stokes Equations with Slip Boundary Conditions in an Infinite Pipe. Acta Applicandae Mathematicae 76, 1–15 (2003). https://doi.org/10.1023/A:1022835216091
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DOI: https://doi.org/10.1023/A:1022835216091