Mathematical Topics In Fluid Mechanics Volume 2 Compressible Models
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Mathematical Topics In Fluid Mechanics Volume 2 Compressible Models
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Author : Pierre-Louis Lions
language : en
Publisher: Oxford University Press
Release Date : 1996
Mathematical Topics In Fluid Mechanics Volume 2 Compressible Models written by Pierre-Louis Lions and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Language Arts & Disciplines categories.
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.
Mathematical Topics In Fluid Mechanics Volume 1 Incompressible Models
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Author : Pierre-Louis Lions
language : en
Publisher: Clarendon Press
Release Date : 1996-06-27
Mathematical Topics In Fluid Mechanics Volume 1 Incompressible Models written by Pierre-Louis Lions and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-27 with Science categories.
One of the most challenging topics in applied mathematics over the past decades has been the development of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc. lead to such equations when formulated in mathematical terms. However despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contains many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena.
Introduction To The Mathematical Theory Of Compressible Flow
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Author : Antonín Novotny
language : en
Publisher: OUP Oxford
Release Date : 2004-06-17
Introduction To The Mathematical Theory Of Compressible Flow written by Antonín Novotny and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-17 with Mathematics categories.
This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.
Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model
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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2015-11-19
Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Mathematics categories.
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Topics In Hyposonic Flow Theory
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Author : Radyadour Kh. Zeytounian
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
Topics In Hyposonic Flow Theory written by Radyadour Kh. Zeytounian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Science categories.
Hyposonic fluid flows, characterized by a low Mach number, are mainly linked with geophysical and environmental fluid flows. In addition they are relevant to engineers because of their connection with aerodynamics. The books brings together insights derived from mathematically rigorous results and combines them with a number of realistic fluid flow situations. Asymptotic analytic solutions for the low-Mach number cases are developed to provide both insights into the underlying physics as well as benchmarks for numerical computations.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2005-10-05
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-05 with Mathematics categories.
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
Advances In Mathematical Fluid Mechanics
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Author : Josef Malek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Mathematical Fluid Mechanics written by Josef Malek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Navier Stokes Fourier Equations
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Author : Radyadour Kh. Zeytounian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-26
Navier Stokes Fourier Equations written by Radyadour Kh. Zeytounian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-26 with Technology & Engineering categories.
This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.
Mathematical Fluid Mechanics
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Author : Jiri Neustupa
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Mathematical Fluid Mechanics written by Jiri Neustupa and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.
Geometry And Nonlinear Partial Differential Equations
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Author : Shing-Tung Yau
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Geometry And Nonlinear Partial Differential Equations written by Shing-Tung Yau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book presents the proceedings of a conference on geometry and nonlinear partial differential equations dedicated to Professor Buqing Su in honor of his one-hundredth birthday. It offers a look at current research by Chinese mathematicians in differential geometry and geometric areas of mathematical physics. It is suitable for advanced graduate students and research mathematicians interested in geometry, topology, differential equations, and mathematical physics.