Mathematical Topics in Fluid Mechanics

by Pierre-Louis Lions

Overview

One of the most challenging topics in applied mathematics is the development of the theory of nonlinear partial different equations. Many problems in mechanics, geometry, and probability lead to such equations when formulated in mathematical terms. Yet despite a long history of contributions, no core theory has been formulated. Written by the winner of the 1994 Fields Medal, this outstanding two-volume work helps shed new light on this important topic. Volume 1 emphasizes the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, a profound and self-contained study of both the classical Navier-Stokes equations (including the inhomogeneous case) and the Euler equations is given. Results about the existence and regularity of solutions are presented with complete proofs. The text highlights in particular the use of modern analytical tools and methods, and it indicates many open problems. Mathematical Topics in Fluid Mechanics will be an indispensable reference for every researcher in the field. Its topicality and the clear, concise presentations by the author make it an outstanding contribution to the great theoretical problems concerning mathematical modelling of physical phenomena.

Product Details

ISBN-13:	9780198514879
Publisher:	Oxford University Press
Publication date:	08/29/1996
Series:	Oxford Lecture Series in Mathematics and Its Applications , #3
Edition description:	New Edition
Pages:	252
Product dimensions:	6.38(w) x 9.50(h) x 0.76(d)

Table of Contents

PrefaceTable of contents1. Presentation of the modelsPart 1: Incompressible Models2. Density-dependent Navier-Stokes equations3. Navier-Stokes equations4. Euler equations and other incompressible modelsAppendix A Truncation of divergence-free vectorfieldsAppendix B Two facts on D1,2(R2)Appendix C Compactness in time with values in weak topologiesAppendix D Weak L1 estimates for solutions of the heat equationAppendix E A short proof of the existence of renormalized solutions for parabolic equationsIntended Table of Contents of Volume 2Part 2: Compressible Models5. Compactness results for compressible isentropic Navier-Stokes6. Stationary problems7. Existence results8. Related questionsPart 3: Asymptotic limites9. Asymptotic limits