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Mathematics > Analysis of PDEs

arXiv:2211.11496 (math)
[Submitted on 21 Nov 2022]

Title:Blow up criteria for a fluid dynamical model arising in astrophysics

Authors:Donatella Donatelli, Lorenzo Pescatore
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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.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35Q30 (76N10, 76V05)
Cite as: arXiv:2211.11496 [math.AP]
  (or arXiv:2211.11496v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2211.11496

Submission history

From: Lorenzo Pescatore [view email]
[v1] Mon, 21 Nov 2022 14:33:31 UTC (28 KB)
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