GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

doi:10.1007/s10473-019-0109-6

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 119-126.doi: 10.1007/s10473-019-0109-6

GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

许兰喜, 李紫奕

Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China

收稿日期:2017-09-26 修回日期:2018-05-22 出版日期:2019-02-25 发布日期:2019-11-14
通讯作者: Ziyi LI E-mail:liziyi@mail.buct.edu.cn
作者简介:Lanxi XU,E-mail:xulx@mail.buct.edu.cn
基金资助:
This work was supported by National Natural Science Foundation Project (41671229).

GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

Lanxi XU, Ziyi LI

Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China

Received:2017-09-26 Revised:2018-05-22 Online:2019-02-25 Published:2019-11-14
Contact: Ziyi LI E-mail:liziyi@mail.buct.edu.cn
Supported by:
This work was supported by National Natural Science Foundation Project (41671229).

摘要/Abstract

摘要： Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π² + LeC, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.

关键词: energy method, energy functional, nonlinear stability, diffusive convection, porous medium

Abstract: Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π² + LeC, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.

Key words: energy method, energy functional, nonlinear stability, diffusive convection, porous medium

许兰喜, 李紫奕. GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM[J]. 数学物理学报(英文版), 2019, 39(1): 119-126.

Lanxi XU, Ziyi LI. GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM[J]. Acta mathematica scientia,Series B, 2019, 39(1): 119-126.

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GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE DIFFUSIVE CONVECTION IN POROUS MEDIUM

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