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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, Rochester, NY, 14627, USA

    Kazuo Yamazaki

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  1. Kazuo Yamazaki
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Correspondence to Kazuo Yamazaki.

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The author expresses gratitude to the Referee for valuable suggestions and comments.

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Yamazaki, K. Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System. Appl Math Optim 79, 1–40 (2019). https://doi.org/10.1007/s00245-017-9419-z

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