scholarly journals Stationary Navier–Stokes equations with non-homogeneous boundary condition in the unbounded domain

2011 ◽  
Vol 52 ◽  
pp. 28-33
Author(s):  
Kristina Kaulakytė
Keyword(s):  
Boundary Condition ◽  
Boundary Problem ◽  
Unbounded Domain ◽  
Stokes System ◽  
Stokes Equations ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in the unbounded domain. The extension of the boundary value satisfying Leray’s inequality is constructed. Therefore the non-homogeneous boundary problem could be reduced to the homogeneous one which was already investigated before.

scholarly journals Stationary Navier–Stokes equations with non-homogeneous boundary condition in a system of two connected layers

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Kaulakytė
Keyword(s):  
Boundary Condition ◽  
Boundary Problem ◽  
Stokes System ◽  
Stokes Equations ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in domain which consists of two connected layers. The extension of the boundary value, which reduces the non-homogeneous boundary problem to the homogeneous one, is constructed in this paper.

scholarly journals In-Flow and Out-Flow Problem for the Stokes System

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer
Keyword(s):  
Stokes System ◽  
Flow Problem ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Tangential Component ◽  
Regularity Of Solutions ◽  
Navier Stokes ◽  
Lateral Part ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

AbstractWe investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.

On nonhomogeneous boundary value problems for the stationary Navier–Stokes equations in two-dimensional symmetric semi-infinite outlets

2015 ◽  
Vol 15 (04) ◽  
pp. 543-569 ◽  
Author(s):  
M. Chipot ◽  
K. Kaulakytė ◽  
K. Pileckas ◽  
W. Xue
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Domain Boundary ◽  
Boundary Value ◽  
Symmetric Domain ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Dirichlet Integral ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

We study the stationary nonhomogeneous Navier–Stokes problem in a two-dimensional symmetric domain with a semi-infinite outlet (for instance, either paraboloidal or channel-like). Under the symmetry assumptions on the domain, boundary value and external force, we prove the existence of at least one weak symmetric solution without any restriction on the size of the fluxes, i.e. the fluxes of the boundary value [Formula: see text] over the inner and the outer boundaries may be arbitrarily large. Only the necessary compatibility condition (the total flux is equal to zero) has to be satisfied. Moreover, the Dirichlet integral of the solution can be finite or infinite depending on the geometry of the domain.

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