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Finite-Time Splash in Free Boundary Problem of 3D Neo-Hookean Elastodynamics
Wei Zhang, Jie Fu, Chengchun Hao
https://arxiv.org/abs/2508.08751 https://arxi…

Finite-Time Splash in Free Boundary Problem of 3D Neo-Hookean Elastodynamics
This paper establishes finite-time splash singularity formation for 3D viscous incompressible neo-Hookean elastodynamics with free boundaries. The system features mixed stress-kinematic conditions where viscous-elastic stresses balance pressure forces at the evolving interface -- a configuration generating complex boundary integrals that distinguish it from Navier-Stokes or MHD systems. To address this challenge, we employ a Lagrangian framework inspired by Coutand and Shkoller (2019), developi…