Blow-up criterion to the compressible full Navier-Stokes equations with inflow-outflow boundary conditions

We investigate the compressible Navier-Stokes equations with heat conduction subject to inflow/outflow boundary conditions, establishing the existence of a strong solution. The primary contribution of this work lies in the derivation of a new regularity criterion for three-dimensional compressible flows, which serves as an analogue to the Beale-Kato-Majda criterion for incompressible fluids. Notably, our findings refine both the strong solution results established by Valli and Zajaczkowski and the conditional regularity framework proposed by Basaric, Feireisl, and Mizerova. Our analysis extends the framework of Basaric, Feireisl, and Mizerova, allowing us to successfully derive the required uniform estimates.