Nonstandard Methods for Stochastic Fluid Mechanics

by Marek Capiński, Nigel J. Cutland

This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by 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 nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition 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.
Contents: Standard PreliminariesNonstandard PreliminariesLoeb Measure and Integration TheoryWeak Solutions of Navier-Stokes EquationsStatistical Solutions of Navier-Stokes EquationsStochastic Navier-Stokes EquationsStatistical Solutions of Stochastic Navier-Stokes EquationsThe Euler Equation
Readership: Applied mathematicians and theoretical physicists.

246 pages, ebook

First published January 1, 1995