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

  • Lorenzo Giacomelli
  • Felix Otto
Original article

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 \(\Gamma\)-limit of suitably rescaled time-discretized Hele-Shaw flows in half space.

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lorenzo Giacomelli
    • 1
  • Felix Otto
    • 2
  1. 1.Dipartimento Me.Mo.Mat., Università di Roma “La Sapienza”, via Scarpa 16, 00161 Roma, Italy (e-mail: giacomelli@dmmm.uniromA1.it)IT
  2. 2.Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 10, 53115 Bonn, GermanyDE

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