Boundary conditions for steady flows of viscoelastic fluids

2008 ◽  
pp. 133-138
Author(s):  
Michael Renardy
Keyword(s):  
Boundary Conditions ◽  
Viscoelastic Fluids ◽  
Steady Flows

EXISTENCE RESULTS FOR FLOWS OF SLIGHTLY COMPRESSIBLE VISCOELASTIC FLUIDS IN A BOUNDED DOMAIN WITH CORNERS

2012 ◽  
Vol 10 (04) ◽  
pp. 381-411
Author(s):  
COLETTE GUILLOPÉ ◽  
ZAYNAB SALLOUM ◽  
RAAFAT TALHOUK
Keyword(s):  
Fixed Point Theory ◽  
Weighted Sobolev Spaces ◽  
Viscoelastic Fluids ◽  
Point Theory ◽  
Small Data ◽  
Steady Flows ◽  
Slightly Compressible ◽  
Linearized Problem ◽  
Uniqueness Of The Solution ◽  
Dimensional Domain

Steady flows of slightly compressible viscoelastic fluids of Oldroyd's type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces [Formula: see text], where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇φ.

scholarly journals Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle

2005 ◽  
Vol 4 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Colette Guillopé ◽  
◽  
Abdelilah Hakim ◽  
Raafat Talhouk ◽  
◽  
...  
Keyword(s):  
Viscoelastic Fluids ◽  
Steady Flows ◽  
Slightly Compressible
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