Spherically Symmetric Solutions of Multi-dimensional Zero-pressure Gas Dynamics System

TL;DR

This paper derives explicit spherically symmetric solutions for multidimensional zero-pressure gas dynamics and adhesion models, analyzing their asymptotic behavior and solutions under various domain conditions.

Contribution

It provides explicit formulas for solutions of the zero-pressure gas dynamics system and its adhesion approximation, including asymptotic analysis and solutions with mass-based conditions.

Findings

Explicit formulas for spherically symmetric solutions

Asymptotic behavior of solutions studied

Solutions with mass conditions analyzed

Abstract

In this article we find explicit formulae for spherically symmetric solutions of the multidimensional zero-pressure gas dynamics system and its adhesion approximation. The asymptotic behaviour of the explicit solutions of the adhesion approximation has been studied. The radial components of the velocity and density satisfy a simpler equation which enables us to get explicit formulae for different types of domains and study its asymptotic behaviour. A class of solutions for the inviscid system with conditions on the mass instead of conditions at origin has also been analyzed.