Mechanics and Mathematics of Fluids of the Differential Type PDF Download

Author: D. Cioranescu
Publisher: Springer
ISBN: 3319393308
Category : Science
Languages : en
Pages : 400

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Book Description
This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book. Each part of the book can be considered as being self-contained. The first part of the book is devoted to a description of the mechanics, thermodynamics, and stability of flows of fluids of grade 2 and grade 3. The second part of the book is dedicated to the development of rigorous mathematical results concerning the equations governing the motion of a family of fluids of the differential type. Finally, the proofs of a number of useful results are collected in an appendix.

Author: Jose Francisco Rodrigues
Publisher: CRC Press
ISBN: 1000158039
Category : Mathematics
Languages : en
Pages : 282

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Book Description
This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.

Author: Pierre-Louis Lions
Publisher: Oxford University Press
ISBN: 9780198514886
Category : Language Arts & Disciplines
Languages : en
Pages : 370

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Book Description
Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

Author: Herbert Amann
Publisher: Birkhäuser
ISBN: 3034809395
Category : Mathematics
Languages : en
Pages : 478

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Book Description
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

Author: Josef Malek
Publisher: Springer Science & Business Media
ISBN: 3642573088
Category : Mathematics
Languages : en
Pages : 232

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Book Description
This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equa tions for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equa and three tions for compressible fluids. The global (in time) analysis of two dimensional motions of compressible fluids were left open for many years.

Author: Richard E. Meyer
Publisher: Courier Corporation
ISBN: 0486151409
Category : Science
Languages : en
Pages : 196

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Book Description
Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. Geared toward advanced undergraduate and graduate students of mathematics and science; prerequisites include calculus and vector analysis. 1971 edition.

Author: Eduard Feireisl
Publisher: Birkhäuser
ISBN: 3319448358
Category : Mathematics
Languages : en
Pages : 189

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Book Description
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.

Author: Giovanni P. Galdi
Publisher: Birkhäuser
ISBN: 3034884249
Category : Mathematics
Languages : en
Pages : 300

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Book Description
This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.

Author: A. R. Paterson
Publisher: Cambridge University Press
ISBN: 9780521274241
Category : Mathematics
Languages : en
Pages : 544

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Book Description
This book introduces the subject of fluid dynamics from the first principles.

Author: Alexandre J. Chorin
Publisher: Springer Science & Business Media
ISBN: 1461208831
Category : Science
Languages : en
Pages : 180

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Book Description
A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.