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Nonstationary Stokes system in Besov spaces
Author(s) -
Zadrzyńska Ewa,
Zajączkowski Wojciech M.
Publication year - 2014
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/mma.2796
Subject(s) - mathematics , besov space , uniqueness , bounded function , mathematical analysis , stokes problem , partition (number theory) , boundary value problem , domain (mathematical analysis) , helmholtz equation , interpolation space , combinatorics , thermodynamics , biochemistry , chemistry , physics , functional analysis , finite element method , gene
We examine the solvability in Besov spacesB r , θ σ , σ ∕ 2of an initial–boundary value problem for the nonstationary Stokes system with the slip boundary conditions. We prove the existence and uniqueness of solutions to the problem in a bounded domain Ω ⊂ R 3 . The existence is shown by localizing the system to interior and boundary subdomains of Ω. The localized Stokes system is transformed by the Helmholtz–Weyl decomposition to the heat and the Poisson equations, which are solved in the Besov spaces. Next, by the properties of the partition of unity and a perturbation argument, the existence is proved in domain Ω. Copyright © 2013 John Wiley & Sons, Ltd.