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Stochastic Navier-Stokes Equations

Stochastic Navier-Stokes Equations The purpose of this article is to survey some results related to the theory of stochastic Navier-Stokes equations (SNSE). The interest of SNSE arises from modelling turbulence. We begin to show how SNSE can be introduced intuitively from the random motion of particles. We then review briefly the deterministic theory and present the main core of existence theory for NSE. We also discuss uniqueness issues. We end up by showing how the splitting-up method provides a useful constructive approach to existence, and by presenting some extensions, like weakening assumptions or considering the special case of small initial data. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Stochastic Navier-Stokes Equations

Bensoussan, A.
Acta Applicandae Mathematicae , Volume 38 (3) – Dec 31, 2004
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References (14)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00996149
Publisher site
See Article on Publisher Site

Abstract

The purpose of this article is to survey some results related to the theory of stochastic Navier-Stokes equations (SNSE). The interest of SNSE arises from modelling turbulence. We begin to show how SNSE can be introduced intuitively from the random motion of particles. We then review briefly the deterministic theory and present the main core of existence theory for NSE. We also discuss uniqueness issues. We end up by showing how the splitting-up method provides a useful constructive approach to existence, and by presenting some extensions, like weakening assumptions or considering the special case of small initial data.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Dec 31, 2004

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