The Navier-Stokes Equations: An Elementary Functional Analytic Approach

The primary objective of this monograph is to develop an elementary and se- contained approach to the mathematical theory of a viscous incompressible fluid n in a domain— of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the first two chapters we collect, without proof some fundamental properties of Sobolev spaces, di...