Abstract
We examine the solvability in Besov spaces of 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 . 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.
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