Mathematical Topics in Fluid Mechanics: Volume 1: Incompressible Models (Oxford Lecture Series in Mathematics and Its Applications)

Book Details

• Publisher: Oxford University Press

• Author: Lions, Pierre-Louis

• Language: English

• Edition: Reprint

• ISBN: 9780199679218

• Pages: 252

• Binding: Paperback

• Release Date: 18-04-2013

About The Book

"Mathematical Topics in Fluid Mechanics" by Pierre-Louis Lions is a foundational two-volume work that delves into the mathematical analysis of fluid mechanics, specifically focusing on systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. As one of the foremost challenges in applied mathematics, the theory of nonlinear partial differential equations has significant implications across various fields, including mechanics, geometry, and probability.

Volume 1 concentrates on the mathematical analysis of incompressible models, providing a self-contained study of the classical Navier-Stokes equations, including their inhomogeneous case, and the Euler equations. The book presents a wealth of results, many of which are new, offering detailed proofs and comprehensive discussions on the existence and regularity of solutions. The text is particularly notable for its application of modern analytical tools and methods, and it highlights numerous open problems in the field.

This work is written by one of the leading researchers in nonlinear partial differential equations and is an indispensable reference for researchers in fluid mechanics and related areas. Its accessible presentation, combined with rigorous mathematical treatment, makes it a crucial resource for those engaged in the mathematical modeling of physical phenomena.

The book has received widespread acclaim for its clarity, depth, and comprehensive analysis, making it a must-read for anyone in the field of theoretical fluid mechanics and nonlinear differential equations. Volume 2, which focuses on compressible models, is highly anticipated for its equally rigorous approach to current research frontiers.