Mathematical Topics in Fluid Mechanics
Volume 1: Incompressible Models
Series: Oxford Lecture Series in Mathematics and Its Applications;
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Product details:
- Publisher OUP Oxford
- Date of Publication 18 April 2013
- ISBN 9780199679218
- Binding Paperback
- No. of pages252 pages
- Size 232x156x14 mm
- Weight 390 g
- Language English
- Illustrations b/w illustrations 0
Categories
Short description:
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.
MoreLong description:
One of the most challenging topics in applied mathematics over the past decades has been the developent 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 inhomogenous 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.
A lot of results are new, and for each of these recent results the complete and self-contained proofs are given...Summarizing the impression of this interesting book, it is worth pointing out that it is written in an easy-reading fashion along with the deep and comprehensive analysis of the topics which are at the highest level of the importance in the modern theory of nonlinear differential equations
Table of Contents:
Preface
Table of contents
Presentation of the models
Part 1: Incompressible Models
Density-dependent Navier-Stokes equations
Navier-Stokes equations
Euler equations and other incompressible models
Appendix A Truncation of divergence-free vectorfields
Appendix B Two facts on D1,2(R2)
Appendix C Compactness in time with values in weak topologies
Appendix D Weak L1 estimates for solutions of the heat equation
Appendix E A short proof of the existence of renormalized solutions for parabolic equations
Intended Table of Contents of Volume 2
Part 2: Compressible Models
Compactness results for compressible isentropic Navier-Stokes
Stationary problems
Existence results
Related questions
Part 3: Asymptotic limites
Asymptotic limits
