scholarly journals ON SINGULAR SOLUTIONS OF THE STATIONARY NAVIER-STOKES SYSTEM IN POWER CUSP DOMAINS

2021 ◽  
Vol 26 (4) ◽  
pp. 651-668
Author(s):  
Konstantinas Pileckas ◽  
Alicija Raciene
Keyword(s):  
Asymptotic Expansion ◽  
Stokes System ◽  
Boundary Value ◽  
Singular Solutions ◽  
Navier Stokes ◽  
Asymptotic Decomposition ◽  
Dirichlet Integral ◽  
Existence Of A Solution ◽  
Source Sink ◽  
Formal Asymptotic Expansion

The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.

scholarly journals A Nonhomogeneous Boundary Value Problem for Steady State Navier-Stokes Equations in a Multiply-Connected Cusp Domain

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2022
Author(s):  
Kristina Kaulakytė ◽  
Konstantinas Pileckas
Keyword(s):  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Singular Part ◽  
Navier Stokes ◽  
Connected Components ◽  
Dirichlet Integral ◽  
Existence Of A Solution ◽  
Flow Rates ◽  
Multiply Connected

The boundary value problem for the steady Navier–Stokes system is considered in a 2D multiply-connected bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with nonzero flow rates over connected components of the boundary is studied. It is also supposed that there is a source/sink in O. In this case the solution necessarily has an infinite Dirichlet integral. The existence of a solution to this problem is proved assuming that the flow rates are “sufficiently small” . This condition does not require the norm of the boundary data to be small. The solution is constructed as the sum of a function with the finite Dirichlet integral and a singular part coinciding with the asymptotic decomposition near the cusp point.

scholarly journals Non-stationary Navier–Stokes equations in 2D power cusp domain

2021 ◽  
Vol 10 (1) ◽  
pp. 982-1010
Author(s):  
Konstantin Pileckas ◽  
Alicija Raciene
Keyword(s):  
Asymptotic Expansion ◽  
Singular Point ◽  
Stokes Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Existence Of A Solution ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

Abstract The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. The case of the boundary value with a nonzero flow rate is considered. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first part of the paper the formal asymptotic expansion of the solution near the singular point is constructed. The justification of the asymptotic expansion and the existence of a solution are proved in the second part of the paper.

scholarly journals ON COUPLED PROBLEMS FOR VISCOUS FLOW IN EXTERIOR DOMAINS

1998 ◽  
Vol 08 (04) ◽  
pp. 657-684 ◽  
Author(s):  
M. FEISTAUER ◽  
C. SCHWAB
Keyword(s):  
Stokes Flow ◽  
Stokes System ◽  
Stokes Problem ◽  
Large Data ◽  
Transmission Conditions ◽  
Navier Stokes ◽  
Coupled Problems ◽  
Exterior Domains ◽  
Existence Of A Solution ◽  
Coupled Problem

The use of the complete Navier–Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier–Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled with the interior Navier–Stokes problem via suitable transmission conditions on the artificial interface between the interior and exterior domains. Our choice of the transmission conditions ensures the existence of a solution of the coupled problem, also for large data.

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.

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