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An Introduction to the Mathematical Theory of the Navier-Stokes Equations

Volume I: Linearised Steady Problems

  • Giovanni P. Galdi

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 38)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Giovanni P. Galdi
    Pages 17-99
  3. Giovanni P. Galdi
    Pages 100-181
  4. Giovanni P. Galdi
    Pages 182-243
  5. Giovanni P. Galdi
    Pages 244-303
  6. Giovanni P. Galdi
    Pages 356-430
  7. Back Matter
    Pages 431-465

About this book

Introduction

Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra­ jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig­ nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga­ tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbounded, of their spatial asymptotic behavior. I shall omit other relevant topics like boundary layer theory, stability, bifurcation, de­ tailed analysis of the behavior for large times, and free-boundary problems, which are to be considered "advanced" ones. In this sense the present work should be regarded as "introductory" to the matter.

Keywords

Navier-Stokes equation dynamics equation fluid mechanics function

Authors and affiliations

  • Giovanni P. Galdi
    • 1
  1. 1.Istituto di IngegneriaUniversità di FerraraFerraraItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3866-7
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-3868-1
  • Online ISBN 978-1-4757-3866-7
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site