Mathematical Analysis and Numerical Methods for Science and Technology

Volume 6 Evolution Problems II

  • Robert Dautray
  • Jacques-Louis Lions

Table of contents

  1. Front Matter
    Pages I-XII
  2. Robert Dautray, Jacques-Louis Lions
    Pages 1-34
  3. Robert Dautray, Jacques-Louis Lions
    Pages 35-208
  4. Robert Dautray, Jacques-Louis Lions
    Pages 209-416
  5. Back Matter
    Pages 417-485

About this book


The object ofthis chapter is to present a certain number ofresults on the linearised Navier-Stokes equations. The Navier-Stokes equations, which describe the motion of a viscous, incompressible fluid were introduced already, from the physical point of view, in §1 of Chap. IA. These equations are nonlinear. We study here the equations that emerge on linearisation from the solution (u = 0, p = 0). This is an interesting exercise in its own right. It corresponds to the case of a very slow flow, and also prepares the way for the study of the complete Navier-Stokes equations. This Chap. XIX is made up of two parts, devoted respectively to linearised stationary equations (or Stokes' problem), and to linearised evolution equations. Questions of existence, uniqueness, and regularity of solutions are considered from the variational point of view, making use of general results proved elsewhere. The functional spaces introduced for this purpose are themselves of interest and are therefore studied comprehensively.


behavior calculus differential equation evolution geophysics knowledge mathematical analysis mathematics mechanics model modeling numerical methods partial differential equation

Authors and affiliations

  • Robert Dautray
    • 1
  • Jacques-Louis Lions
    • 2
  1. 1.ParisFrance
  2. 2.Collège de FranceParis Cedex 5France

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66102-3
  • Online ISBN 978-3-642-58004-8
  • Buy this book on publisher's site