Skip to main content

Mathematical Preliminaries

  • Chapter
Micropolar Fluids

Abstract

In this chapter, for the convenience of the reader, we recall some basic mathematical notions and theorems that we shall often use in the following chapters. To a number of important theorems and lemmas we provide proofs, especially when they are straightforward and simple enough or when we find them very instructive. We also clarify some notions, providing examples, special cases, and exercises. We believe that the best illustration of the few abstract theorems from functional analysis stated in this chapter, that may seem too abstract at the first reading, is provided in the subsequent chapters through their direct application to concrete problems in partial differential equations of hydrodynamics. Thus, if a theorem seems too abstract, we advice the reader to skip it without becoming discouraged and then concentrate on Section 1 in Chapter 2, which contains fundamental material for this part of the book.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Łukaszewicz, G. (1999). Mathematical Preliminaries. In: Micropolar Fluids. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0641-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0641-5_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6851-2

  • Online ISBN: 978-1-4612-0641-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics