scholarly journals Nonhomogeneous boundary value problems for stationary Navier–Stokes equations in a multiply connected bounded domain

2009 ◽  
Vol 243 (1) ◽  
pp. 127-150 ◽  
Author(s):  
Hideo Kozono ◽  
Taku Yanagisawa
Keyword(s):  
Boundary Value Problems ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Boundary Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multiply Connected ◽  
Nonhomogeneous Boundary ◽  
Stationary Navier Stokes Equations

scholarly journals ON NONHOMOGENEOUS BOUNDARY VALUE PROBLEM FOR THE STATIONARY NAVIER-STOKES EQUATIONS IN A SYMMETRIC CUSP DOMAIN

2021 ◽  
Vol 26 (1) ◽  
pp. 55-71
Author(s):  
Kristina Kaulakytė ◽  
Neringa Klovienė
Keyword(s):  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Navier Stokes ◽  
Cusp Point ◽  
Multiply Connected Domain ◽  
Navier Stokes Equations ◽  
Multiply Connected ◽  
Nonhomogeneous Boundary ◽  
Stationary Navier Stokes Equations

The nonhomogeneous boundary value problem for the stationary NavierStokes equations in 2D symmetric multiply connected domain with a cusp point on the boundary is studied. It is assumed that there is a source or sink in the cusp point. A symmetric solenoidal extension of the boundary value satisfying the LerayHopf inequality is constructed. Using this extension, the nonhomogeneous boundary value problem is reduced to homogeneous one and the existence of at least one weak symmetric solution is proved. No restrictions are assumed on the size of fluxes of the boundary value.

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