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Steady-State Navier–Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis

Author

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  • Rita Juodagalvytė

    (Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania
    Institute Camille Jordan UMR (CNRS 5208), University Jean-Monnet, 23 Rue P. Michelon, 42023 Saint-Etienne, France)

  • Grigory Panasenko

    (Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania
    Institute Camille Jordan UMR (CNRS 5208), University Jean-Monnet, 23 Rue P. Michelon, 42023 Saint-Etienne, France)

  • Konstantinas Pileckas

    (Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania)

Abstract

Steady-state Navier–Stokes equations in a thin tube structure with the Bernoulli pressure inflow–outflow boundary conditions and no-slip boundary conditions at the lateral boundary are considered. Applying the Leray–Schauder fixed point theorem, we prove the existence and uniqueness of a weak solution. An asymptotic approximation of a weak solution is constructed and justified by an error estimate.

Suggested Citation

  • Rita Juodagalvytė & Grigory Panasenko & Konstantinas Pileckas, 2021. "Steady-State Navier–Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis," Mathematics, MDPI, vol. 9(19), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2433-:d:647532
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