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Applied Mathematics & Optimization

, Volume 79, Issue 1, pp 1–40 | Cite as

Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System

  • Kazuo YamazakiEmail author
Article
  • 90 Downloads

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.

Keywords

Determining modes Ergodicity Micropolar fluid Navier–Stokes equations Stationary measure 

Mathematics Subject Classification

35Q35 37L55 60H15 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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