Finite-time collapse and soliton-like states in the dynamics of dissipative gases

TL;DR

This paper investigates the finite-time blowup and formation of soliton-like states in the dynamics of dissipative gases, highlighting the role of heat diffusion in smoothing singularities and extending previous planar flow results.

Contribution

It introduces exact localized soliton solutions for dissipative gas dynamics where heat diffusion balances nonlinear cooling, generalizing earlier planar flow studies.

Findings

Finite-time density blowup in the absence of diffusion.

Existence of exact soliton-like solutions balancing diffusion and cooling.

Diffusive processes smoothen singularities in gas density.

Abstract

A study of the gas dynamics of a dilute collection of the inelastically colliding hard spheres is presented. When diffusive processes are neglected the gas density blows up in a finite time. The blowup is the mathematical expression for one of the possible mechanisms for cluster formation in dissipative gases. The way diffusive processes smoothen the singularity has been studied. Exact localized soliton-type solutions of the gas dynamics when heat diffusion balances non-linear cooling are obtained. The presented results generalize previous findings for planar flows.