Well-posedness of the free boundary problem for incompressible elastodynamics

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)7844-7889
Journal / PublicationJournal of Differential Equations
Issue number12
Online published17 Dec 2018
Publication statusPublished - 5 Jun 2019


The free boundary problem for the three dimensional incompressible elastodynamics system is studied under the Rayleigh–Taylor sign condition. Both the columns of the elastic stress FFI and the transpose of the deformation gradient FI are tangential to the boundary which moves with the velocity, and the pressure vanishes outside the flow domain. The linearized equation takes the form of wave equation in terms of the flow map in the Lagrangian coordinate, and the local-in-time existence of a unique smooth solution is proved using a geometric argument in the spirit of [19].

Research Area(s)

  • Elastodynamics, Free boundary problem, Incompressible