Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models
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Beschreibung
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.
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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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 Includes supplementary material: sn.pub/extras
Autor*in
Franck Boyer
Themen in »Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models«
Analysis of nonlinear parabolic equations Incompressible Stokes and Navier-Stokes equations Renormalized solutions of the transport equation outflow boundary conditions partial differential equations fluid- and aerodynamics
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From the reviews:
“This book is a valuable contribution to the theory of Navier-Stokes equations and related models. It contains important existence, uniqueness and stability results, together with a rigorous analysis of all treated problems. It is warmly recommended to all researchers interested in modern nonlinear problems in fluid mechanics.” (Mirela Kohr, zbMATH, Vol. 1286, 2014)()