Mathematical tools for the study of the incompressible Navier-Stokes equations and related models

Franck Boyer (1) , Pierre Fabrie (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Analysis of nonlinear parabolic equations; Incompressible Stokes and Navier-Stokes equations

Domaines: Equations aux dérivées partielles [math.AP]

Franck Boyer, Pierre Fabrie. Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. Springer New York, pp.538, 2012, Applied Mathematical Sciences, 978-1-4614-5974-3. ⟨10.1007/978-1-4614-5975-0⟩. ⟨hal-00777731⟩