Nonstandard Methods for Stochastic Fluid Mechanics (Advances in Mathematics for Applied Sciences)

This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by a nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations. The authors provide a self-contained introduction to the nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to Navier-Stokes equations. The subsequent expositon shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.