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 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.

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. .

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.

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.

Peyresq Lectures On Nonlinear Phenomena Volume Ii

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Author : Jacques-alexandre Sepulchre
language : en
Publisher: World Scientific
Release Date : 2003-05-20

Peyresq Lectures On Nonlinear Phenomena Volume Ii written by Jacques-alexandre Sepulchre and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-20 with Science categories.

This book is the second volume of lecture notes on various topics in nonlinear physics delivered by specialists in the field who gave courses in the small village of Peyresq (France) during summer schools (2000, 2001, 2002) organised by the Institut Non Linéaire de Nice (INLN), in collaboration with the Institut de Recherche de Physique Hors Equilibre (IRPHE). The goal is to provide good summaries on the state of the art of some domains in physics having the common denominator of belonging to nonlinear sciences, and to promote the transfer of knowledge between them.

Numerical Models For Differential Problems

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-22

Numerical Models For Differential Problems written by Alfio Quarteroni 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 2010-01-22 with Mathematics categories.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.