ENERGY STABILITY FOR THERMO-VISCOUS FLUIDS WITH A FADING MEMORY HEAT FLUX

被引：2

作者：

Amendola, Giovambattista ^{[1
]}

Fabrizio, Mauro ^{[2
]}

Golden, John Murrough ^{[3
]}

Manes, Adele ^{[1
]}

机构：

[1] Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[2] Univ Bologna, Dipartmento Matemat, I-40127 Bologna, Italy

[3] Dublin Inst Technol, Sch Math Sci, Dublin 8, Ireland

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2015年 / 4卷 / 03期

关键词：

Benard problem; viscous fluid with memory; exponential stability;

D O I：

10.3934/eect.2015.4.265

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we consider the thermal convection problem in arbitrary bounded domains of a three-dimensional space for incompressible viscous fluids, with a fading memory constitutive equation for the heat flux. With the help of a recently proposed free energy, expressed in terms of a minimal state functional for such a system, we prove an existence and uniqueness theorem for the linearized problem. Then, assuming some restrictions on the Rayleigh number, we also prove exponential decay of solutions.

引用

页码：265 / 279

页数：15

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