LAUSR

We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-I singularities of solutions with $$\mathop {\lim \sup }\limits_{t \nearrow T} |div(t,x)|(T - t) \leqslant \kappa $$limsupt↗T|div(t,x)|(T−t)≤κ can never happen at time T for all adiabatic number γ > 1. Here κ > 0 does not depend on the initial data. This is achieved by proving the regularity of solutions under $$\rho (t,x) \leqslant \frac{M}{{{{(T - t)}^\kappa }}},M < \infty .$$ρ(t,x)≤M(T−t)κ,M<∞. This new scaling invariance also motivates us to construct an explicit type-II blowup solution for γ > 1.