Weighted coercive estimates of solutions to the Stokes problem in parabolically growing layer
Konstantin I Pileckas, L. Zaleskis · Asymptotic Analysis · 2007
The Stokes problem is studied in the domain Ω⊂R 3 coinciding outside the ball B R ={x∈R 3 : |x| 3 : x ′ =(x 1 , x 2 )∈R 2 , |x 3 | ′ )}, where h(x ′ ) is a smooth function, h(x ′ )≥h 0 >0 ∀x ′ ∈R 2 and h(x ′ )=|x ′ | β ≡r β , β∈(0, 1), for r>1. Coercive estimates of the solution to the Stokes problem are proved in a scale of weighted function spaces with the norm determined by a stepwise anisotropic distribution of weight factors.