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

Rita Juodagalvytė, Grigory Panasenko and Konstantinas Pileckas
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Rita Juodagalvytė: Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania
Grigory Panasenko: Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania
Konstantinas Pileckas: Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, 03225 Vilnius, Lithuania

Mathematics, 2021, vol. 9, issue 19, 1-20

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.

Keywords: Navier–Stokes equations; Bernoulli pressure boundary condition; asymptotic approximation; quasi-Poiseuille flows; boundary layers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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