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local well-posedness of the free boundary incompressible elastodynamics with surface tension

guxumin fujiaoshou（shanghaicaijingdaxue）

tengxunhuiyi id: 503 931 182

consider the incompressible viscoelasticity, a coupling system of the navier-stokes equations for the fluid motion with a transport equation for the deformation tensor. under a natural force balance law on the free boundary with the surface tension, its well-posedness theory has been established for any fixed viscosity coefficient ε > 0. in this talk, we solve the corresponding elastic case on a short time interval, i.e. ε = 0. our method is the vanishing viscosity limit by establishing a uniform a priori estimates with respect to the viscosity. we point out that based on a crucial new observation on the inherent structure of the elastic term on the free boundary, the framework here is established all in standard sobolev spaces, but not the co-normal ones. this is a joint work with prof. zhen lei and prof. fanghua lin.