粘弹性流体被从下面加热时完全充满容器的小的对流运动

H. Essaouini, Fs, Morocco. Tetuan, P. Capodanno
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引用次数: 0

摘要

摘要:在本文中,我们研究了粘弹性流体从下加热并完全填充刚性容器时的小振动,限制在更简单的Oldroyd模型中。利用Boussinesq假设,得到了该问题的算子方程。我们证明了谱的存在性,证明了系统的稳定性,如果运动粘度系数和温度电导率系数足够大,并且存在一组正实特征值,实轴的一个点为积累点。然后,我们证明了该问题可以简化为克林-兰格铅笔的研究,并得到了有关谱的新结果。最后,利用半群理论得到了关联演化问题解的存在性和唯一性定理。
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Small convective motions of a visco-elastic fluid filling completely a container when the fluid is heated from below
Abstract: In this paper, we study the small oscillations of a visco-elastic fluid that is heated from below and fills completely a rigid container, restricting to the more simple Oldroyd model. We obtain the operatorial equations of the problem by using the Boussinesq hypothesis. We show the existence of the spectrum, prove the stability of the system if the kinematic coefficient of viscosity and the coefficient of temperature conductivity are sufficiently large and the existence of a set of positive real eigenvalues having a point of the real axis as point of accumulation. Then, we prove that the problem can be reduced to the study of a Krein-Langer pencil and obtain new results concerning the spectrum. Finally, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of the semigroups theory.
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发文量
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审稿时长
8 weeks
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