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.
Variational formulation for the lubrication approximation of the Hele-Shaw flow / Giacomelli, Lorenzo; F., Otto. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 13:(2001), pp. 377-403. [10.1007/s005260000077]
Variational formulation for the lubrication approximation of the Hele-Shaw flow
GIACOMELLI, Lorenzo;
2001
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
