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The First Boundary Value Problem in a Given Domain

  • Liudas Stupelis
Part of the Mathematics and Its Applications book series (MAIA, volume 326)

Abstract

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.

Keywords

Generalize Solution Differential Operator Space Versus Linear Functional Stokes System 
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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Liudas Stupelis
    • 1
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania

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