Well-posedness of two-dimensional hydroelastic waves with mass
Well-posedness of two-dimensional hydroelastic waves with mass
复制标题
DOI：
10.1016/j.jde.2016.12.016
复制
发表时间：
2017-05-05
影响因子：
2.4
通讯作者：
Ambrose, David M.
中科院分区：
文献类型：
--
作者：
Liu, Shunlian;Ambrose, David M.
本文研究二维无旋流体界面流动中的水弹性波。每一种流体在一个垂直方向上都是无限大的，而在另一个垂直方向上则被一个自由表面所限制。弹性效应被认为是在自由表面;这可以描述的物理设置，如海洋边界以上的一层冰。以前的研究证明了适定性，没有考虑弹性表面的质量;我们现在考虑这个质量的影响。在某个积分方程可解的假设下，证明了系统初值问题的适定性。我们能够证明，在某些情况下，如小质量参数的情况下，积分方程确实是可解的。证明使用几何因变量，归一化弧长参数化，并在演化方程的小规模分解。(C)2016 Elsevier Inc. All rights reserved.
We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved well-posedness without considering the mass of the elastic surface; we now consider the effect of this mass. Under the assumption that a certain integral equation is solvable, we prove well-posedness of the initial value problem for the system. We are able to demonstrate that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. The proof uses geometric dependent variables, a normalized arclength parameterization, and a small-scale decomposition in the evolution equations. (C) 2016 Elsevier Inc. All rights reserved.