On the nonlinear stability of the MHD anisotropic Bénard problem

Palese, Lidia

doi:10.1016/j.ijengsci.2005.03.007

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In [20] the nonlinear stability of the thermodiffusive equilibrium for the magnetohydrodynamic anisotropic Bénard problem is studied by the energy splitting [11], obtaining conditional nonlinear asymptotical stability results.…”

Section: Introductionmentioning

confidence: 99%

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Palese¹

2022

AnnalsARSciMath

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In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting partially ionized fluid in a horizontal layer heated from below. The classical L 2 norm is too weak to evaluate some stabilizing or instabilizing effects of the electroanisotropic currents. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem in terms of the poloidal and toroidal scalar fields. In such a way, if instability occurs as stationary convection, we obtain the coincidence of linear and nonlinear stability bounds.

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Section: Introductionmentioning

confidence: 99%

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Palese¹

2022

AnnalsARSciMath

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“…In the magnetohydrodynamic case, [13], for free boundaries, the coincidence of linear and nonlinear stability parameters was deduced for a fully ionized fluid , i.e., if the conduction diffusion solution is linearly stable, it is conditionally nonlinearly asymptotically stable.…”

Section: Introductionmentioning

confidence: 99%

Thermosolutal convection in a rotating couple-stress uid

Palese

2015

JAM

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In this paper we study the nonlinear Lyapunov stability of the conduction-diusion solution of a rotating couple-stress uid, in a layer heated and salted from below. After reformulating the perturbation evolution equations in a suit- able equivalent form, we derive the appropriate Lyapunov function and we prove that, if the principle of exchange of stabilities holds, the linear and nonlinear stability bounds are equal.The nonlinear stability bound is exactly the critical Rayleigh num-ber obtained solving the linear instability problem of the conduction- diusion solution.

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The Lyapunov–Movchan method in problems of the stability of flows and deformation processes

Георгиевский¹,

Kvachev²

2014

Journal of Applied Mathematics and Mechanics

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On the nonlinear stability of the MHD anisotropic Bénard problem

Cited by 3 publications

References 15 publications

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Thermosolutal convection in a rotating couple-stress uid

The Lyapunov–Movchan method in problems of the stability of flows and deformation processes

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