Nonstationary Stokes system in weighted Sobolev spaces

Abstract

We consider an initial-boundary value problem for nonstationary Stokes system in a bounded domain Omega⊂ℝ3 with slip boundary conditions. We assume that Ω is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms: and where ϱ(x) = dist{x, L}. We proved the result. Given the external force f∈L2, −µ(ΩT), initial velocity v0∈H(Ω), µ∈ℝ+\ℤ there exist velocity v∈H(ΩT) and the pressure p, ∇p∈L2, −µ(ΩT) and a constant c, independent of v, p, f, such that As we consider the Stokes system in weighted Sobolev spaces the following two things must be used: 1. the slip boundary condition and 2. the Helmholtz–Weyl decomposition. Copyright © 2010 John Wiley & Sons, Ltd.