A blow-up criterion in terms of the density for compressible viscous flows
Jishan Fan, Song Jiang and Guoxi Ni
Abstract: We study an initial boundary value problem for the two-dimensional Navier–Stokes equations of compressible fluids in the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum (ρ=0) and the concentration of mass (ρ=∞), then a local strong solution can be continued globally in time.