2022/11/21 by Donatelli, Donatella, Pescatore, Lorenzo
#35Q30 (76N10 #76V05) #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.11496
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.