This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

‘… one of the very few good books that centres on the rigorous mathematical theory of vorticity and incompressible flow … extremely well written and compelling reading … the contents and the cost of this book certainly makes it a good purchase for experienced theoretical fluid dynamists’.

D. B. Ingham Source: Contemporary Physics

‘This book is destined to become a classic … Majda and Bertozzi have produced a formidable and extremely well-written book on this subject that throws out a series of challenges to the modern student … This is the standard to which the rest of us need to aspire.’

Source: Journal of Fluid Mechanics

‘… a masterpiece of applied mathematics.’

Source: Zeitschrift für Angewandte Mathematik und Mechanik