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

Article type: Research Article

Authors: Pileckas, K. | Zaleskis, L.

Affiliations: Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania. E-mail: [email protected] | Vilnius University, Faculty of Mathematics and Informatics, Naugarduko Str., 24, Vilnius, Lithuania

Abstract: The Stokes problem is studied in the domain Ω⊂R3 coinciding outside the ball BR={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≡rβ, 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.

Keywords: stationary Stokes problem, unbounded domains, coercive estimates, weighted function spaces

Journal: Asymptotic Analysis, vol. 54, no. 3-4, pp. 211-233, 2007