New dissipated energies for the thin fluid film equation

被引：15

作者：

Laugesen, RS ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2005年 / 4卷 / 03期

关键词：

thin fluid film; lubrication approximation; energy; entropy; pinch-off; film rupture;

D O I：

10.3934/cpaa.2005.4.613

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The thin fluid film evolution h(t) = -(h(n)h(xxx)), is known to conserve the fluid volume integral h dx and to dissipate the "energies" integral h(1.5-n) dx and f h(x)(2) dx. We extend this last result by showing the energy integral h(p)h(x)(2) dx is dissipated for some values of p < 0, when 1/2 < n < 3. For example when n = 1, the Hele-Shaw equation h(t) = -(hh(xxx))(x) dissipates integral h(-1/2)h(x)(2) dx.

引用

页码：613 / 634

页数：22

共 23 条

[1] Stable and unstable singularities in the unforced Hele-Shaw cell [J].