Variatonal formulation for the lubrication approximation of the Hele-Shaw flow

被引：62

作者：

Giacomelli, L

Otto, F

机构：

[1] Univ Roma La Sapienza, Dipartimento Me Mo Mat, I-00161 Rome, Italy

[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2001年 / 13卷 / 03期

关键词：

Mathematics Subject Classification (2000): 35A15, 49J45, 35K25, 35K55, 35K65, 35R35, 76D27, 76D08, 76A20.;

D O I：

10.1007/s005260000077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It has been recently discovered that both the surface tension driven one-phase Hele-Shaw flow and its lubrication approximation can be understood as (continuous limits of time-discretized) gradient flows of the corresponding surface energy functionals with respect to the Wasserstein metric. Here we complete the connection between the two problems, proving that the time-discretized lubrication approximation is the F-limit of suitably rescaled time-discretized Hele-Shaw flows in half space.

引用

页码：377 / 403

页数：27

共 16 条

[1] Singularity formation in Hele-Shaw bubbles [J].