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Gibbsian Dynamics and Ergodicity of Stochastic Micropolar Fluid System
- Source :
- Applied Mathematics & Optimization. 79:1-40
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
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.
- Subjects :
- 0209 industrial biotechnology
Work (thermodynamics)
Control and Optimization
Series (mathematics)
Applied Mathematics
010102 general mathematics
Ergodicity
Mathematical analysis
02 engineering and technology
01 natural sciences
Measure (mathematics)
Physics::Fluid Dynamics
020901 industrial engineering & automation
Classical mechanics
Fluid dynamics
Periodic boundary conditions
Dumbbell
0101 mathematics
Navier–Stokes equations
Mathematics
Subjects
Details
- ISSN :
- 14320606 and 00954616
- Volume :
- 79
- Database :
- OpenAIRE
- Journal :
- Applied Mathematics & Optimization
- Accession number :
- edsair.doi...........2e089690a08a723267eb6b8f0888d7df