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

by Boyer, Franck.
Authors: Fabrie, Pierre.%author. | SpringerLink (Online service) Series: Applied Mathematical Sciences, 0066-5452 ; . 183 Physical details: XIII, 525 p. online resource. ISBN: 1461459753 Subject(s): Mathematics. | Differential equations, partial. | Hydraulic engineering. | Mathematics. | Partial Differential Equations. | Engineering Fluid Dynamics. | Fluid- and Aerodynamics.
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E-Book E-Book AUM Main Library 515.353 (Browse Shelf) Not for loan

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.-.

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.

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