Effects of Surface Tension on the Stability of Dynamical Liquid-Vapor Interfaces
Effects of Surface Tension on the Stability of Dynamical Liquid-Vapor Interfaces
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DOI：
10.1007/s00205-004-0328-3
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发表时间：
2004-07
影响因子：
2.5
通讯作者：
S. Benzoni-Gavage;H. Freistühler
中科院分区：
文献类型：
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作者：
S. Benzoni-Gavage;H. Freistühler
尖锐的和平坦的界面下的多维扰动的持久性进行了研究，从一个类似的观点Majda的处理经典的冲击。这里的主要新奇之处是，跳跃条件的自由界面考虑到表面张力。这意味着，与经典的跳跃条件不同，它们是非齐次的，包含一阶和二阶微分的前端。简正模分析表明，中性模可以沿着波前传播。在标准设置中，这将意味着弱稳定性结果，涉及导数损失的能量估计。在我们的情况下，缺乏均匀性的基本边值问题意味着中性模式只能是足够大的波长。合适的频率截止，然后产生能量估计没有损失的衍生物-常数系数线性化的问题，在一致稳定的经典冲击的情况下。
The persistence of sharp and flat interfaces under multidimensional perturbations is investigated from a viewpoint analogous to Majda’s treatment of classical shocks. The main novelty here is that jump conditions for the free interfaces take into account surface tension. This means that, unlike classical jump conditions, they are non-homogeneous, containing first-order and second-order differentials of the front. A normal modes analysis shows that neutral modes may propagate along the front. In the standard setting, this would imply a weak stability result, involving energy estimates with loss of derivatives. In our case the lack of homogeneity of the underlying boundary value problem implies that neutral modes can only be of large enough wave length. Suitable frequency cut-offs then yield energy estimates without loss of derivatives – for the constant-coefficients linearized problem, as in the case of uniformly stable classical shocks.