The authors introduce post-collapse Lagrangian perturbation theory (PCPT) that asymptotically captures early post-shell-crossing dynamics in 3D by using high-order LPT until crossing and then 1D pancake results for gravitational backreaction.
Colombi, Phase-space structure of protohalos: Vlasov versus particle-mesh, A&A647, A66 (2021), arXiv:2012.04409 [astro-ph.CO]
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Post-collapse Lagrangian perturbation theory in three dimensions
The authors introduce post-collapse Lagrangian perturbation theory (PCPT) that asymptotically captures early post-shell-crossing dynamics in 3D by using high-order LPT until crossing and then 1D pancake results for gravitational backreaction.