Shell-crossing in quasi-one-dimensional flow

Understand

Blow-up of solutions for the cosmological fluid equations, often dubbed shell-crossing or orbit crossing, denotes the breakdown of the single-stream regime of the cold-dark-matter fluid.

• At this instant, the velocity becomes multi-valued and the density singular.
• Shell-crossing is well understood in one dimension (1D), but not in higher dimensions.
• This paper is about quasi-one-dimensional (Q1D) flow that depends on all three coordinates but differs only slightly from a strictly 1D flow, thereby allowing a perturbative treatment of shell-crossing using the Euler--Poisson equations written in Lagrangian coordinates.