Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport

We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain ⊂ Rd , d ∈ {2, 3}, with no-slip boundary conditions. We first prove the existence and uniqueness of local-in-time strong solutions. Further, we prove a blow-up criterion for the strong solution in terms of L∞-norms for the density and the velocity.