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Mathematics - Dynamical Systems & Differential Equations | Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models

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

Series: Applied Mathematical Sciences, Vol. 183

Boyer, Franck, Fabrie, Pierre

2013, XIV, 526 p.

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  • The book is self-contained
  • The methods presented in the book can be applied to a wide range of domains in nonlinear analysis
  • Some very recent research results are presented along with more classical ones
  • The first chapter of the book presents, with details, the derivation of the equations of fluid mechanics

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.

Content Level » Graduate

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

Related subjects » Classical Continuum Physics - Dynamical Systems & Differential Equations - Mechanics

Table of contents 

Preface.- Contents.- The equations of fluid mechanics.- Analysis tools.- Sobolev spaces.- Steady Stokes equations.- Navier-Stokes equations for homogeneous fluids.- Nonhomogeneous fluids.- Boundary conditions modeling.- Classic differential operators.- Thermodynamics supplement.- References.- Index.-

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