scholarly journals Construction of weak solutions to compressible Navier–Stokes equations with general inflow/outflow boundary conditions via a numerical approximation

2021 ◽  
Author(s):  
Young-Sam Kwon ◽  
Antonin Novotný
Keyword(s):  
Boundary Conditions ◽  
Weak Solutions ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary Conditions ◽  
Outflow Boundary

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

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2433
Author(s):  
Rita Juodagalvytė ◽  
Grigory Panasenko ◽  
Konstantinas Pileckas
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Thin Tube ◽  
Outflow Boundary ◽  
Tube Structure

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.

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