Spherically symmetric collapsing solution in the form of shadow wave

TL;DR

This paper investigates a stable shadow wave solution with unbounded density in a self-gravitating star model, extending results to cases with vanishing pressure, using an isothermal Euler-Poisson system with density-dependent viscosity.

Contribution

It introduces a stable shadow wave solution with unbounded density for the Euler-Poisson system, including the vanishing pressure case, advancing understanding of star collapse models.

Findings

Existence of stable shadow wave solutions with unbounded density.

Extension of results to the vanishing pressure case.

Insights into collapse dynamics of self-gravitating systems.

Abstract

This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that there exists stable shadow wave solution with unbounded density at the origin. This results is extended to the vanishing pressure case.