Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System

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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.

Original languageEnglish
JournalApplied Mathematics and Optimization
Volume79
Issue number1
DOIs
StatePublished - Feb 15 2019

Keywords

  • Determining modes
  • Ergodicity
  • Micropolar fluid
  • Navier–Stokes equations
  • Stationary measure

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