The Navier-Stokes Problem in the 21st Century

Book Details

• Author: Pierre Gilles Lemarié-Rieusset

• Publisher: CRC Press

• Binding: Hardcover

• Edition: 1

• ISBN: 9781466566217

• Pages: 718

• Release Date: 08-03-2016

• Dimensions: 9.4 x 6.1 x 1.7 inches

• Languages: English

About the Book

The Navier–Stokes Problem in the 21st Century offers an in-depth and up-to-date exploration of the Navier-Stokes equation, a critical subject in the field of partial differential equations (PDEs) and one of the Clay Millennium Prize Problems. Despite extensive research on fluid dynamics and turbulence, the complete resolution of the Navier–Stokes equation remains a significant challenge.

This book serves as a comprehensive guide to the role of harmonic analysis in fluid mechanics, specifically focusing on incompressible deterministic Navier–Stokes equations for fluids filling entire space. The work encompasses:

• Classical results on local existence

• Studies on regularity criteria and uniqueness of solutions

• The history and recent progress in the theory

• A focus on Morrey spaces, beneficial for studying weak and mild solutions

It includes references to both the historical development of the equations and active research in the field. The work is designed to offer clarity on current challenges and advancements, from basic concepts to advanced research.

Key Features:

• Detailed historical context and recent breakthroughs

• Focus on mathematical theory, especially harmonic analysis

• Rigorous proofs of important results

• Addresses the famous Navier-Stokes regularity problem

• Ideal for postgraduate students and researchers

The Navier–Stokes Problem in the 21st Century is recommended for anyone working in fluid dynamics, harmonic analysis, or mathematical PDEs. The book's exceptional clarity makes it an invaluable reference for graduate students, researchers, and Ph.D. students seeking a thorough understanding of the Navier-Stokes equations and their implications in modern mathematical research.