# Steady flows, nonlinear gravitostatic waves and Zeldovich pancakes in a Newtonian gas

## TL;DR

This paper explores nonlinear steady solutions in Newtonian hydrodynamics and gravity, revealing universal density singularities, phase-dependent wave regimes, and the existence of subsonic and supersonic gravitostatic waves.

## Contribution

It introduces new nonlinear periodic solutions in Newtonian gas flows, including the universal zero-pressure case and phase-dependent wave behaviors with finite pressure effects.

## Key findings

- Universal lattice of density singularities in zero-pressure case
- Critical density separates in-phase and out-of-phase wave regimes
- Existence of subsonic and supersonic gravitostatic waves

## Abstract

We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is universal: it is a lattice of integrable density singularities coinciding with maxima of the gravitational potential. With finite pressure effects included, there exists critical matter density that separates two regimes of behavior. If the average density is below the critical, the solution is a density wave which is in phase with the wave of the gravitational potential. If the average density is above the critical, the waves of the density and potential are out of phase. Traveling plane gravitostatic waves are also predicted and their properties elucidated. Specifically, subsonic wave is made out of two out of phase oscillations of matter density and gravitational potential. If the wave is supersonic, the density-potential oscillations are in phase.