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.
“This book is destined to become a classic…This is the standard to which the rest of us need to aspire.” Journal of Fluid Mechanics
“There are about 11 books currently available on the market covering incompressible flows. Majda and Bertozzi’s book is unique in covering both the classical and weak solutions for the incompressible and inviscid flows and is excellently done.” Mathematical Reviews