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引用次数: 0
摘要
由第一位作者提出的基于所谓全局关系的方法,最近导致推导出一个新的非线性积分微分方程,该方程描述了表面张力不为零的萨夫曼-泰勒手指经典问题的特征。在表面张力为零的特殊情况下,该方程满足 Saffman 和 Taylor 所获得的显式解。在此,我们首先针对表面张力为零的情况,提出一个新的非线性积分微分方程来描述 Saffman-Taylor 手指的特征。然后,通过使用对表面张力为零的特殊情况有效的 Saffman-Taylor 显式解,我们证明上述方程产生了一组显著的积分三角等式。
The Saffman–Taylor problem and several sets of remarkable integral identities
The methodology based on the so-called global relation, introduced by the first author, has recently led to the derivation of a novel nonlinear integral-differential equation characterizing the classical problem of the Saffman–Taylor fingers with nonzero surface tension. In the particular case of zero surface tension, this equation is satisfied by the explicit solution obtained by Saffman and Taylor. Here, first, for the case of zero surface tension, we present a new nonlinear integrodifferential equation characterizing the Saffman–Taylor fingers. Then, by using the explicit Saffman–Taylor solution valid for the particular case of zero surface tension, we show that the above equations give rise to sets of remarkable integral trigonometric identities.
期刊介绍:
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.