UNCONDITIONAL NONLINEAR EXPONENTIAL STABILITY OF THE MOTIONLESS CONDUCTION-DIFFUSION SOLUTION

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2000,（2）
• 页码范围: 113-120
• 页数: 8页
• 语种: 英文

摘要

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 = PC/PT _＜ 1, α = C/R ＞ 1 the motionless state is always stable and for τ＜ 1, α ＜ 1 the sufficient and necessary conditions for stability coincide, where PC, PT, C and R are the Schmidt number, Prandtl number,Rayleigh number for solute and heat, respectively. Moreover, the criteria guarantees the exponential stability.