Mathematical Topics In Fluid Mechanics Volume 1 Incompressible 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
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Author : Pierre-Louis Lions
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
Mathematical Topics In Fluid Mechanics written by Pierre-Louis Lions and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no central core theory. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models.
Mathematical Topics In Fluid Mechanics
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Author : Pierre-Louis Lions
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
Mathematical Topics In Fluid Mechanics written by Pierre-Louis Lions and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no central core theory. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models.
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models
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Author : Franck Boyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models written by Franck Boyer 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 2012-11-06 with Mathematics categories.
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. .
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.
Fluids Under Pressure
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Author : Tomáš Bodnár
language : en
Publisher: Springer Nature
Release Date : 2020-04-30
Fluids Under Pressure written by Tomáš Bodnár and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-30 with Mathematics categories.
This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
Handbook Of Mathematical Fluid Dynamics
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Author : S. Friedlander
language : en
Publisher: Elsevier
Release Date : 2007-05-16
Handbook Of Mathematical Fluid Dynamics written by S. Friedlander and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-16 with Science categories.
This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.
Incompressible Bipolar And Non Newtonian Viscous Fluid Flow
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Author : Hamid Bellout
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Incompressible Bipolar And Non Newtonian Viscous Fluid Flow written by Hamid Bellout 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 2013-11-19 with Science categories.
The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
Navier Stokes Equations
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Author : Grzegorz Łukaszewicz
language : en
Publisher: Springer
Release Date : 2016-04-12
Navier Stokes Equations written by Grzegorz Łukaszewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-12 with Mathematics categories.
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
New Trends And Results In Mathematical Description Of Fluid Flows
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Author : Miroslav Bulíček
language : en
Publisher: Springer
Release Date : 2018-09-26
New Trends And Results In Mathematical Description Of Fluid Flows written by Miroslav Bulíček and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-26 with Mathematics categories.
The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field ofmathematical fluid mechanics.