Notes on INS (21): Majda-Bertozzi book

The book by Andrew Majda & Andrea Bertozzi, Vorticity and Incompressible Flow, 2002, 600+ pp,  is one of the best books on the Navier-Stokes problem. Compared to other books (Temam, Constantin & Foias, Lemarié …), this book is less technical and more geometrical (and hence much easier to read, at least for me), though it also contains necessary analytical tools (e.g. Sobolev  interpolation inequalities) for the proof of existence and regularity results.

The book presents the Navier-Stokes equation (and the Euler equation) from the point of view of vortex dynamics. Instead of looking at the equation for the velocity field, one looks at the equation for the vorticity field (which is equivalent to the Navier-Stokes equation). One should probabaly understand the vortexes (its formation, development, depletion, …) in order to study regularity/singularity of the Navier-Stokes equation.

The electronic version of this book is available online.

Editorial review:

“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

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