Existence results for Hele–Shaw flow driven by surface tension
Existence results for Hele–Shaw flow driven by surface tension
复制标题
表面张力驱动的 Hele-Shaw 流的存在性结果
DOI：
--
复制
发表时间：
1998
影响因子：
1.9
通讯作者：
G. Prokert
中科院分区：
文献类型：
--
作者：
G. Prokert
研究了以表面张力为驱动机制的N维Hele-Shaw流问题解的短时存在性和唯一性。证明了该方程解的整体存在性和在平衡点附近解的指数衰减性。这些结果是在s足够大的Sobolev空间Hs中得到的。的主要工具是扰动的一个固定的参考域，线性化相对于这些扰动，一个quasilinearization参数的基础上的几何不变性，和先验能量估计。
This paper addresses short-time existence and uniqueness of a solution to the N-dimensional Hele–Shaw flow problem with surface tension as driving mechanism. Global existence in time and exponential decay of the solution near equilibrium are also proved. The results are obtained in Sobolev spaces Hs with sufficiently large s. The main tools are perturbations of a fixed reference domain, linearization with respect to these perturbations, a quasilinearization argument based on a geometric invariance property, and a priori energy estimates.