Premium
The Two‐Dimensional Exterior Stokes Problem, Existence, Regularity and Decay Properties
Author(s) -
Neugebauer Maria Specovius
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960510)19:7<507::aid-mma779>3.0.co;2-r
Subject(s) - mathematics , uniqueness , sobolev space , stokes problem , mathematical analysis , pure mathematics , mathematical physics , physics , finite element method , thermodynamics
The Stokes problem −Δ u +∇ p = f , div u = g in Ω, u ∣ ∂Ω = h is investigated for two‐dimensional exterior domains Ω. By means of potential theory, existence, uniqueness and regularity results for weak solutions are proved in weighted Sobolev spaces with weights proportional to ∣ x ∣ δ as ∣ x ∣→∞. For f = 0, g = 0, explicit decay formulas are obtained for the solutions u and p . Finally, the results are compared with the theory of r ‐generalized solutions, i.e. ∇ u ∈ L r .