Global Solvability in W 2 2,1 -Weighted Spaces of the Two-Dimensional Navier–Stokes Problem in Domains with Strip-Like Outlets to Infinity

2007 ◽  
Vol 10 (2) ◽  
pp. 272-309 ◽  
Author(s):  
Konstantin Pileckas
Keyword(s):  
Stokes Problem ◽  
Global Solvability ◽  
Weighted Spaces ◽  
Navier Stokes ◽  
Two Dimensional

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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