Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models

  • Franck Boyer
  • Pierre Fabrie

Part of the Applied Mathematical Sciences book series (AMS, volume 183)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Franck Boyer, Pierre Fabrie
    Pages 1-48
  3. Franck Boyer, Pierre Fabrie
    Pages 49-120
  4. Franck Boyer, Pierre Fabrie
    Pages 121-228
  5. Franck Boyer, Pierre Fabrie
    Pages 229-343
  6. Franck Boyer, Pierre Fabrie
    Pages 345-407
  7. Franck Boyer, Pierre Fabrie
    Pages 409-452
  8. Franck Boyer, Pierre Fabrie
    Pages 453-506
  9. Back Matter
    Pages 507-525

About this book


The objective of this self-contained book is two-fold. First, the reader is introduced  to the modelling and  mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems.

The background needed  are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject.


Analysis of nonlinear parabolic equations Incompressible Stokes and Navier-Stokes equations Renormalized solutions of the transport equation outflow boundary conditions

Authors and affiliations

  • Franck Boyer
    • 1
  • Pierre Fabrie
    • 2
  1. 1., Laboratoire d'Analyse Topologie et ProbaFaculté des sciences et techniques de SaMARSEILLEFrance
  2. 2., Institut de Mathématiques de BordeauxENSEIRB-MATMECA, Institut PolytechniqueTalenceFrance

Bibliographic information