Description

Book Synopsis
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.

Table of Contents
Standard Preliminaries; Nonstandard Preliminaries; Weak Solutions of Navier-Stokes Equations; Statistical Solutions of Navier-Stokes Equations; Stochastic Navier-Stokes Equations; Other Equations of Hydromechanics; Euler Equation.

Nonstandard Methods For Stochastic Fluid

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    A Hardback by Marek Capinski, Nigel J Cutland

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 01/03/1995
      ISBN13: 9789810217105, 978-9810217105
      ISBN10: 9810217102

      Description

      Book Synopsis
      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.

      Table of Contents
      Standard Preliminaries; Nonstandard Preliminaries; Weak Solutions of Navier-Stokes Equations; Statistical Solutions of Navier-Stokes Equations; Stochastic Navier-Stokes Equations; Other Equations of Hydromechanics; Euler Equation.

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