# Stochastic micromodel of the Couette flow

@article{Malyshev2011StochasticMO, title={Stochastic micromodel of the Couette flow}, author={Viktor Aleksandrovich Malyshev and Anatoly Manita}, journal={arXiv: Mathematical Physics}, year={2011} }

We study Markov exclusion process for a particle system with a local interaction in the integer strip. This process models the exchange of velocities and particle-hole exchange of the liquid molecules. It is shown that the mean velocity profile corresponds to the behaviour which is characteristic for incompressible viscous liquid. We prove the existence of phase transition between laminar and turbulent profiles.

## 8 Citations

### Large-scale flows of viscous incompressible vortical fluid

- Physics
- 2015

An exact solution of the Navier - Stokes equations is given that describes the vorticity of a viscous incompressible liquid or gas, dissipative mediums, stationary shear counter-current of continuous…

### Large-scale flows of viscous incompressible vortical fluid

- PhysicsRussian Aeronautics (Iz VUZ)
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An exact solution of the Navier - Stokes equations is given that describes the vorticity of a viscous incompressible liquid or gas, dissipative mediums, stationary shear counter-current of continuous…

### Unsteady layered vortical fluid flows

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An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette…

### Unsteady layered vortical fluid flows

- Physics
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An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette…

### Exact solutions of the Navier–Stokes equations for describing an isobaric one-directional vertical vortex flow of a fluid

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The article proposes a family of exact solutions to the Navier–Stokes equations for describing isobaric inhomogeneous unidirectional fluid motions. Due to the incompressibility equation, the velocity…

### Exact Solutions for a Couette–hiemenz Creeping Convective Flow with Linear Temperature Distribution on the Upper Boundary

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A new exact solution is found for the plane convection of a viscous incompressible fluid describable by the Oberbeck–Boussinesq equation system in an infinite thin layer. The solution of the…

### Asymptotics of stationary measure under scaling in stochastic exchange processes

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Asymptotic properties of an invariant distribution of exchange processes are studied on a two-dimensional lattice with fixed boundary conditions.

### On mathematical models of the service networks

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In this short review, queueing theory relations with other mathematical disciplines and different applied problems are followed.

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