Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models [electronic resource] / by Franck Boyer, Pierre Fabrie.
Contributor(s): Fabrie, Pierre [author.] | SpringerLink (Online service)Material type: TextSeries: Applied Mathematical Sciences: 183Publisher: New York, NY : Springer New York : Imprint: Springer, 2013Description: XIV, 526 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781461459750Subject(s): Mathematics | Partial differential equations | Fluids | Fluid mechanics | Mathematics | Partial Differential Equations | Engineering Fluid Dynamics | Fluid- and AerodynamicsAdditional physical formats: Printed edition:: No titleDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access online
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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.