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Reviews and research articles summarizing a wide range of active research topics in fluid mechanics.
Book Synopsis Partial Differential Equations and Fluid Mechanics by : James C. Robinson
Download or read book Partial Differential Equations and Fluid Mechanics written by James C. Robinson and published by Cambridge University Press. This book was released on 2009-07-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews and research articles summarizing a wide range of active research topics in fluid mechanics.
The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
Book Synopsis Partial Differential Equations in Fluid Mechanics by : Charles L. Fefferman
Download or read book Partial Differential Equations in Fluid Mechanics written by Charles L. Fefferman and published by Cambridge University Press. This book was released on 2018-09-27 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.
This book concerns partial differential equations applied to fluids problems in science and engineering.
Book Synopsis Partial Differential Equations in Fluid Dynamics by : Isom H. Herron
Download or read book Partial Differential Equations in Fluid Dynamics written by Isom H. Herron and published by Cambridge University Press. This book was released on 2008-07-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns partial differential equations applied to fluids problems in science and engineering.
For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
Book Synopsis Energy Methods for Free Boundary Problems by : S.N. Antontsev
Download or read book Energy Methods for Free Boundary Problems written by S.N. Antontsev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.
Book Synopsis Large-Scale PDE-Constrained Optimization in Applications by : Subhendu Bikash Hazra
Download or read book Large-Scale PDE-Constrained Optimization in Applications written by Subhendu Bikash Hazra and published by Springer Science & Business Media. This book was released on 2009-12-16 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.
This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Book Synopsis Partial Differential Equations in Mechanics 2 by : A.P.S. Selvadurai
Download or read book Partial Differential Equations in Mechanics 2 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.
Book Synopsis Singular Limits in Thermodynamics of Viscous Fluids by : Eduard Feireisl
Download or read book Singular Limits in Thermodynamics of Viscous Fluids written by Eduard Feireisl and published by Springer Science & Business Media. This book was released on 2009-03-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.
Now available in English for the first time, Physics and Partial Differential Equations, Volume I bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.
Book Synopsis Physics and Partial Differential Equations by : Tatsien Li
Download or read book Physics and Partial Differential Equations written by Tatsien Li and published by SIAM. This book was released on 2013-08-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in English for the first time, Physics and Partial Differential Equations, Volume I bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.
For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
Book Synopsis Energy Methods for Free Boundary Problems by : S.N. Antontsev
Download or read book Energy Methods for Free Boundary Problems written by S.N. Antontsev and published by Springer Science & Business Media. This book was released on 2001-10-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.
