Mechanics And Mathematics Of Fluids Of The Differential Type
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| Author | : D. Cioranescu |
| Publisher | : Springer |
| Total Pages | : 400 |
| Release | : 2016-07-29 |
| Genre | : Science |
| ISBN | : 3319393308 |
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 |
| Total Pages | : 280 |
| Release | : 2020-10-02 |
| Genre | : Mathematics |
| ISBN | : 1000115232 |
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 | : James C. Robinson |
| Publisher | : Cambridge University Press |
| Total Pages | : 275 |
| Release | : 2012-10-18 |
| Genre | : Mathematics |
| ISBN | : 1139577212 |
The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
| Author | : Rutherford Aris |
| Publisher | : Courier Corporation |
| Total Pages | : 322 |
| Release | : 2012-08-28 |
| Genre | : Mathematics |
| ISBN | : 048613489X |
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
| Author | : Eduard Feireisl |
| Publisher | : Birkhäuser |
| Total Pages | : 189 |
| Release | : 2016-11-25 |
| Genre | : Mathematics |
| ISBN | : 3319448358 |
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 | : A. R. Paterson |
| Publisher | : Cambridge University Press |
| Total Pages | : 544 |
| Release | : 1983-11-10 |
| Genre | : Mathematics |
| ISBN | : 9780521274241 |
This book introduces the subject of fluid dynamics from the first principles.
| Author | : Franz Durst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 728 |
| Release | : 2008-09-01 |
| Genre | : Science |
| ISBN | : 3540713425 |
Fluid mechanics embraces engineering, science, and medicine. This book’s logical organization begins with an introductory chapter summarizing the history of fluid mechanics and then moves on to the essential mathematics and physics needed to understand and work in fluid mechanics. Analytical treatments are based on the Navier-Stokes equations. The book also fully addresses the numerical and experimental methods applied to flows. This text is specifically written to meet the needs of students in engineering and science. Overall, readers get a sound introduction to fluid mechanics.
| Author | : Tsutomu Kambe |
| Publisher | : World Scientific |
| Total Pages | : 403 |
| Release | : 2007 |
| Genre | : Science |
| ISBN | : 9812706674 |
This textbook describes the fundamental OC physicalOCO aspects of fluid flows for beginners of fluid mechanics in physics, mathematics and engineering, from the point of view of modern physics. It also emphasizes the dynamical aspects of fluid motions rather than the static aspects, illustrating vortex motions, waves, geophysical flows, chaos and turbulence. Beginning with the fundamental concepts of the nature of flows and the properties of fluids, the book presents fundamental conservation equations of mass, momentum and energy, and the equations of motion for both inviscid and viscous fluids. In addition to the fundamentals, this book also covers water waves and sound waves, vortex motions, geophysical flows, nonlinear instability, chaos, and turbulence. Furthermore, it includes the chapters on superfluids and the gauge theory of fluid flows. The material in the book emerged from the lecture notes for an intensive course on Elementary Fluid Mechanics for both undergraduate and postgraduate students of theoretical physics given in 2003 and 2004 at the Nankai Institute of Mathematics (Tianjin) in China. Hence, each chapter may be presented separately as a single lecture."
| Author | : Carlo Marchioro |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 295 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461242843 |
Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi cult new mathematical {::oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.
| Author | : Igor Gaissinski |
| Publisher | : CRC Press |
| Total Pages | : 658 |
| Release | : 2018-06-13 |
| Genre | : Mathematics |
| ISBN | : 1351029045 |
This volume is dedicated to modeling in fluid mechanics and is divided into four chapters, which contain a significant number of useful exercises with solutions. The authors provide relatively complete references on relevant topics in the bibliography at the end of each chapter.
