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Preliminaries

  • Grigory Panasenko,
  • Konstantin Pileckas

摘要

Chapter Preliminaries presents the essential notations and concepts from real and functional analysis. It introduces the spaces of smooth functions, Sobolev spaces, and spaces of divergence-free vector-valued functions. In particular, the results on the asymptotic behavior of solutions of the Stokes equations in domains with noncompact boundary and cylindrical outlets to infinity are presented. References to specialized literature are provided.