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Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System

Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System The theory of micropolar fluids emphasizes the micro-structure of fluids by coupling the Navier–Stokes equations with micro-rotational velocity, and is widely viewed to be well fit, better than the Navier–Stokes equations, to describe fluids consisting of bar-like elements such as liquid crystals made up of dumbbell molecules or animal blood. Following the work of Weinan et al. (Commun Math Phys 224:83–106, 2001), we prove the existence of a unique stationary measure for the stochastic micropolar fluid system with periodic boundary condition, forced by only the determining modes of the noise and therefore a type of finite-dimensionality of micropolar fluid flow. The novelty of the manuscript is a series of energy estimates that is reminiscent from analysis in the deterministic case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System

Applied Mathematics and Optimization , Volume 79 (1) – May 10, 2017

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References (49)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-017-9419-z
Publisher site
See Article on Publisher Site

Abstract

The theory of micropolar fluids emphasizes the micro-structure of fluids by coupling the Navier–Stokes equations with micro-rotational velocity, and is widely viewed to be well fit, better than the Navier–Stokes equations, to describe fluids consisting of bar-like elements such as liquid crystals made up of dumbbell molecules or animal blood. Following the work of Weinan et al. (Commun Math Phys 224:83–106, 2001), we prove the existence of a unique stationary measure for the stochastic micropolar fluid system with periodic boundary condition, forced by only the determining modes of the noise and therefore a type of finite-dimensionality of micropolar fluid flow. The novelty of the manuscript is a series of energy estimates that is reminiscent from analysis in the deterministic case.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 10, 2017

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