A global attracting set for nonlocal Kuramoto–Sivashinsky equations arising in interfacial electrohydrodynamics
A global attracting set for nonlocal Kuramoto–Sivashinsky equations arising in interfacial electrohydrodynamics
复制标题
界面电流体动力学中出现的非局域 Kuramoto-Sivashinsky 方程的全局吸引集
DOI：
10.1017/s0956792506006760
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发表时间：
2006
影响因子：
1.9
通讯作者：
D. Papageorgiou
中科院分区：
文献类型：
--
作者：
D. Tseluiko;D. Papageorgiou
我们研究了一类广义的非局域演化方程，它包括了带电薄膜沿倾斜平面流动的模型中的那些方程，以及在通过界面湍流强化传热或传质方面的应用。证明了整体存在唯一性结果，并根据方程的参数(系统长度和无量纲电场测量参数乘以非定域项)得到了吸收球半径的精确估计。将所建立的估计值与方程的数值解进行了比较，进而提出了吸收球半径的最佳上界。一个标度参数被用来解释这一点，一个普遍的猜想是基于大量的计算得出的。
We study a generalized class of nonlocal evolution equations which includes those arising in the modelling of electrified film flow down an inclined plane, with applications in enhanced heat or mass transfer through interfacial turbulence. Global existence and uniqueness results are proved and refined estimates of the radius of the absorbing ball in $L^2$ are obtained in terms of the parameters of the equations (the length of the system and the dimensionless electric field-measuring parameter multiplying the nonlocal term). The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this and a general conjecture is made based on extensive computations.