Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects
Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects
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DOI：
10.4310/cms.2013.v11.n2.a15
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发表时间：
2012-04
期刊：
影响因子：
--
通讯作者：
Hao-qing Wu;Xiang Xu
中科院分区：
文献类型：
--
作者：
Hao-qing Wu;Xiang Xu
在本文中，我们研究了具有热致马兰戈尼效应的两种粘性不可压缩牛顿流体混合物的扩散界面模型的适定性和长期动力学。控制系统由修正的纳维-斯托克斯方程以及相场和能量传输方程组成。我们首先推导出能量不等式，该能量不等式说明了在初始温度变化很小的假设下系统的耗散性质。然后我们通过能量法建立了弱/强解的存在性，并讨论了系统的长期动力学和稳定性。
In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Marangoni effects. The governing system consists of modified Navier--Stokes equations coupled with phase-field and energy transport equations. We first derive an energy inequality that illustrates the dissipative nature of the system under the assumption that the initial temperature variation is properly small. Then we establish the existence of weak/strong solutions via the energy method and discuss the long-time dynamics as well as stability of the system.