This volume is devoted to the study of the Navier-Stokes equations providing a comprehensive
reference for a range of applications: from advanced undergraduate students to engineers and
professional mathematicians involved in research on fluid mechanics dynamical systems and
mathematical modeling. Equipped with only a basic knowledge of calculus functional analysis
and partial differential equations the reader is introduced to the concept and applications of
the Navier-Stokes equations through a series of fully self-contained chapters. Including lively
illustrations that complement and elucidate the text and a collection of exercises at the end
of each chapter this book is an indispensable accessible classroom-tested tool for teaching
and understanding the Navier-Stokes equations.Incompressible Navier-Stokes equations describe
the dynamic motion (flow) of incompressible fluid the unknowns being the velocity and pressure
as functions of location (space) and time variables. A solution to these equations predicts the
behavior of the fluid assuming knowledge of its initial and boundary states. These equations
are one of the most important models of mathematical physics: although they have been a subject
of vivid research for more than 150 years there are still many open problems due to the nature
of nonlinearity present in the equations. The nonlinear convective term present in the
equations leads to phenomena such as eddy flows and turbulence. In particular the question of
solution regularity for three-dimensional problem was appointed by Clay Institute as one of the
Millennium Problems the key problems in modern mathematics. The problem remains challenging
and fascinating for mathematicians and the applications of the Navier-Stokes equations range
from aerodynamics (drag and lift forces) to the design of watercraft and hydroelectric power
plants to medical applications such as modeling the flow of blood in the circulatory system.
