The First Boundary Value Problem in a Given Domain
This chapter discusses the first boundary value problem for the Stokes system in bounded sectionaly-smooth domains and the Navier—Stokes system in domains with noncompact boundaries. Properties of differential operators in Hölder, weighted Hölder, and weighted Sobolev spaces are studied in Sections 4.1–4.3. In Section 4.4, we present a simple proof that the first boundary value problem for the Stokes system in a bounded three-dimensional domain, whose boundary consists of two smooth components intersecting under a non-zero varying angle, has a unique solution in weighted Sobolev spaces.
KeywordsGeneralize Solution Differential Operator Space Versus Linear Functional Stokes System
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