Mathematical topics in fluid mechanics
著者
書誌事項
Mathematical topics in fluid mechanics
（Oxford lecture series in mathematics and its applications）
Clarendon Press, 2013, c1996
- v. 1
- v. 2
大学図書館所蔵 件 / 全4件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
v. 1. Incompressible models -- v. 2. Compressible models
Includes index
"First published in paperback 2013"
内容説明・目次
- 巻冊次
-
v. 1 ISBN 9780199679218
内容説明
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.
目次
- Preface
- Table of contents
- 1. Presentation of the models
- Part 1: Incompressible Models
- 2. Density-dependent Navier-Stokes equations
- 3. Navier-Stokes equations
- 4. 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
- 5. Compactness results for compressible isentropic Navier-Stokes
- 6. Stationary problems
- 7. Existence results
- 8. Related questions
- Part 3: Asymptotic limites
- 9. Asymptotic limits
- 巻冊次
-
v. 2 ISBN 9780199679225
内容説明
This second volume works with the first to form a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations such as the incompressible and compressible NavierStokes equations. The main emphasis in the first volume is on the mathematical analysis of incompressible models. The second volume is an attempt to achieve a mathematical understanding of compressible
Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes unique material on compactness properties of solutions for the Cauchy problem, the existence and regularity of stationary solutions, and the existence of global weak solutions.
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.
目次
PART II: COMPRESSIBLE MODELS
「Nielsen BookData」 より