Download Free Mathematical Topics In Fluid Mechanics Volume 2 Compressible Models Book in PDF and EPUB Free Download. You can read online Mathematical Topics In Fluid Mechanics Volume 2 Compressible Models and write the review.

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.
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.
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.
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.
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.
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.
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 of mathematical fluid mechanics.
Mathematical Theory of Compressible Fluid Flow covers the conceptual and mathematical aspects of theory of compressible fluid flow. This five-chapter book specifically tackles the role of thermodynamics in the mechanics of compressible fluids. This text begins with a discussion on the general theory of characteristics of compressible fluid with its application. This topic is followed by a presentation of equations delineating the role of thermodynamics in compressible fluid mechanics. The discussion then shifts to the theory of shocks as asymptotic phenomena, which is set within the context of rational mechanics. The remaining two chapters is a thorough description of the hodograph method. These chapters provide a comparison of the modern integration theories. The features, characteristics, and application of transonic flow are also explored. This book is an ideal advanced textbook for both graduate students and research workers.
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.
This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.