The Three-Dimensional Navier–Stokes Equations

This book offers a thorough introduction to the mathematical theory of the Navier–Stokes equations, ideal for graduate students and researchers alike.

This book, The Three-Dimensional Navier–Stokes Equations, serves as a comprehensive yet approachable introduction to the mathematical theory surrounding the three-dimensional Navier–Stokes equations. It presents a self-contained exploration of key results, many of which are typically found only in specialized research papers. The author meticulously covers significant achievements in the field, such as the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions. Additionally, it discusses the conditional local regularity results established by Serrin and others, alongside the partial regularity results from Caffarelli, Kohn, and Nirenberg.

The book includes several appendices that provide essential background material and proofs of standard results that are often difficult to locate in other literature. This makes The Three-Dimensional Navier–Stokes Equations not only a valuable textbook for graduate courses spanning one or two semesters but also a beneficial resource for professionals engaged in mathematical fluid dynamics. Each chapter is supplemented with numerous exercises, complete with full solutions at the end, ensuring that students can practice and solidify their understanding of the concepts.

Overall, The Three-Dimensional Navier–Stokes Equations stands out as the only introductory text that thoroughly addresses all mainstream results in detail. Its rigorous yet accessible approach makes it an essential addition to the library of any graduate student or researcher in the field of fluid dynamics.