Asymptotic analysis for Korteweg models
Asymptotic analysis for Korteweg models
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Korteweg 模型的渐近分析
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
C. Rohde
中科院分区：
文献类型：
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作者：
W. Dreyer;J. Giesselmann;C. Kraus;C. Rohde
本文讨论了等温Navier-Stokes-Korteweg方程组的一个锐界面极限。尖锐的界面极限是由匹配的渐近展开的领域在幂的界面宽度e。这些膨胀被认为是在界面区域（内膨胀）和在散装（外膨胀），并匹配顺序顺序。特别地，我们考虑了相应的内部方程的第一阶通过在界面层中的坐标的变化。对于一个特定的缩放，我们建立这些内部方程的可解性标准，并恢复在一般设置的跳跃条件的尖锐界面模型的结果。
This paper deals with a sharp interface limit of the isothermal Navier-Stokes-Korteweg system. The sharp interface limit is performed by matched asymptotic expansions of the fields in powers of the interface width e. These expansions are considered in the interfacial region (inner expansions) and in the bulk (outer expansion) and are matched order by order. Particularly we consider the first orders of the corresponding inner equations obtained by a change of coordinates in an interfacial layer. For a specific scaling we establish solvability criteria for these inner equations and recover the results within the general setting of jump conditions for sharp interface models.