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Nonstationary Stokes system in weighted Sobolev spaces

✍ Scribed by Wojciech M. Zaja̧czkowski

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
283 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

We consider an initial-boundary value problem for nonstationary Stokes system in a bounded domain ⊂ R 3 with slip boundary conditions. We assume that is crossed by an axis L. Let us introduce the following weighted Sobolev spaces with finite norms:

, where

x) = dist{x, L}. We proved the result. Given the external force f ∈ L 2,-( T ), initial velocity v 0 ∈ H 1 -( ), ∈ R + \Z there exist velocity v ∈ H 2,1 -( T ) and the pressure p, ∇p ∈ L 2,-( T ) and a constant c, independent of v, p, f, such that v H 2,1 -( T ) + ∇p L 2,-( T ) c( f L 2,-( T ) + v 0 H 1 -( ) ).

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.

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