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Variational formulation for the lubrication approximation of the Hele-Shaw flow
Lorenzo Giacomelli and Felix OttoAbstract
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
- Received:
- 09.05.00
- Published:
- 09.05.00
- MSC Codes:
- 35A15, 49J45, 35K25, 35K55, 35K65, 35R35, 76D27, 76D08, 76A20
- Keywords:
- variational methods, gamma-convergence, higher order nonlinear degenerate parabolic equations, free boundary problems, hele-shaw flow, lubrication theory, thin fluid films