Weighted coercive estimates of solutions to the Stokes problem in parabolically growing layer

Abstract

The Stokes problem is studied in the domain Ω⊂R³ coinciding outside the ball B_R={x∈R³: |x|<R} with the parabolically growing layer Ω={x∈R³: x^′=(x₁, x₂)∈R², |x₃|<h(x^′)}, where h(x^′) is a smooth function, h(x^′)≥h₀>0 ∀x^′∈R² 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.