|Title||Invariant manifold theory for hydrodynamic transition|
|Publisher||Longman Scientific & Technical|
|Year of publication||1991|
|Reviewed by||Balan Vladimir|
Invariant manifold theory for the Navier-Stokes equations provides an active link between the theory of finite dimensional dynamical systems and the onset dynamics of turbulence. The volume develops such a theory for hydrodynamic motions in bounded containers.
The main results include spectral and analyticity theorems for semigroups and invariant manifolds. Although the main focus is on bounded domains, there are discussed extensions to unbounded domains in each section of the work and are pointed out open problems.
The book also includes two appendices: one concerned with Ladyzhenskaya's theory of global attractors for two-dimensional viscous flows in bounded domains, and one in which are derived certain implications of group action on the invariant manifold theory. The style is rigorous and the presented results are at advanced level. The theorems are accompanied by detailed proofs and figures. Also, the volume has a concise table of contents, a bibliography of almost 100 titles and an index of notions.
The book is intended for scientists working in chaos and turbulence theory. Control theorists with interests in stabilizing and controlling particular solutions of the Navier-Stokes equations will also find this book useful.
Therefore, it represents a good investment for researchers and graduate students in chaos, turbulence theory, hydrodynamic stability, dynamical systems, partial differential equations and control theory.