Abstract
We consider the free boundary problem for the flow of an incompressible inviscid elastic fluid. The columns of the deformation gradient are tangent and the pressure vanishes along the free interface. We prove the local existence of a unique smooth solution to the free boundary problem under the mixed type stability condition, provided that the Rayleigh-Taylor sign condition is satisfied at all the points of the initial interface where the non-collinearity condition for the deformation gradient (among three columns of the deformation gradient there are two non-collinear vectors) fails. In particular, we solve an open problem proposed by Y. Trakhinin in the paper [29] under the incompressible setting.
Published Version
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