Remarks on the rate of decay of solutions to linearized compressible Navier-Stokes equations

We consider the Lp−Lq estimates of solutions to the Cauchy problem of linearized compressible Navier–Stokes equation. Especially, we investigate the diffusion wave property of the compressible Navier–Stokes flows, which was studied by D. Hoff and K. Zumbrum and Tai-P. Liu and W. Wang. 1. Introduction. In this paper, we consider the Cauchy problem of the following linearized compressible Navier-Stokes equations: ρt + γdiv v = 0 in (0,∞) × Rn,(1.1) vt − α∆v − β∇div v + γ∇ρ = 0 in (0,∞) × Rn