Stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders

Quan Wang

doi:10.3934/dcdsb.2014.19.543

Article Contents

2014, Volume 19, Issue 2: 543-563. Doi: 10.3934/dcdsb.2014.19.543

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Stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders

Quan Wang^1,

1.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610021

Received: May 31, 2013

Revised: September 30, 2013

Published: February 2014

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Abstract

In this paper, our objective is to apply the attractor bifurcation theory to study the stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders. We get a dimensionless parameter $T$ which can describe the stability and bifurcation of the plasma fluid through calculation. When $T$ is smaller than a critical number $T_0$, the plasma fluid is stable. When $T$ crosses the critical number $T_0$, the plasma fluid becomes unstable and will generate a new magnetic field which has an interesting structure.

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Mathematics Subject Classification: Primary: 76W05, 76U05, 82D10; Secondary: 37N20, 37G30, 37G35.

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