Blow up criteria for a fluid dynamical model arising in astrophysics

TL;DR

This paper establishes criteria for the blow-up of local strong solutions in a complex astrophysical fluid model, linking solution breakdown to key physical quantities like velocity gradient and temperature.

Contribution

It introduces a blow-up criterion for a coupled compressible viscous fluid model with vacuum, extending classical results to astrophysical hydrodynamics.

Findings

Blow-up criterion in terms of velocity gradient, mass fraction gradient, and temperature.

Existence of local strong solutions with vacuum in an astrophysical fluid model.

Extension of Beale-Kato-Majda criterion to compressible, heat-conductive, self-gravitating fluids.

Abstract

In this paper we deal with the existence of local strong solution for a perfect compressible viscous fluid, heat conductive and self gravitating, coupled with a first order kinetics used in astrophysical hydrodynamical models. In our setting the vacuum is allowed and as a byproduct of the existence result we get a blow-up criterion for the local strong solution. Moreover we prove a blow-up criterion for the local strong solutions in terms of the velocity gradient, the mass fraction gradient and the temperature similar to the well known Beale-Kato-Majda criterion for ideal incompressible flows.