Unconditional nonlinear exponential stability of the motionless conduction-diffusion solution |
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Authors: | Xu Lanxi |
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Institution: | (1) Department of Mechanics and Engineering Science, State Key Laboratory for Turbulence Research, Peking University, 100871 Beijing, China |
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Abstract: | Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient
is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown
that for τ=P
C
/P
T
≤1,
the motionless state is always stable and for τ≤1,
the sufficient and necessary conditions for stability coincide, whereP
C
,P
T
,C andR are the Schmidt number, Prandtl number, Rayleigh number for solute and heat respectively. Moreover, the criteria guarantees
the exponential stability.
The Project supported by SRF for ROCS, China Postdoctoral Science Foundation and the National Basic Research Project “Nonlinear
Science” |
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Keywords: | poloidal-toroidal decomposition energy method generalized energy nonlinear stability |
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