Optimal decay for the compressible Navier-Stokes equations without additional smallness assumptions

This work is concerned with the large time behavior of solutions to barotropic compressible Navier-Stokes equations in R d ( ≥ 2 ) . A pure energy argument independent spectral analysis has been developed more general L p framework, which enables us not only obtain optimal time-decay rates but also remove smallness low frequencies initial data that required previous studies on this problem. The crucial part proof lies evolution negative Besov norms at frequencies, mainly depends non standard product estimates and some elaborate use Sobolev embeddings interpolations. Our results could hold true case highly oscillating velocities comparison classical efforts.