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

Abstract

We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $\Omega \subset {\mathbb{R}}^d$, $d\in \{2,3\}$, 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 $L^{\infty }$-norms for the density and the velocity.

References in corpus (2)

• Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport
• DMV-strong uniqueness principle for the compressible Navier-Stokes system with potential temperature transport