Remark on the Rate of Decay of Solutions to Linearized Compressible Navier-stokes Equations

ρ0 and v0 are given initial data; α and γ are positive constants and β a nonnegative constant. Concerning the decay property, asymptotically, the solution decomposed into sum of two parts under the influence of a hyperbolic aspect and a parabolic aspect. One of which dominates in Lp for 2 p ∞, the other 1 p < 2. For p 2, the time asymptotic behavior of solutions is similar to the solution of pure diffusion problem. Namely, the decay at the rate of the solution is similar to the solution of a linear, second order, strictly parabolic system with L1 initial data. Moreover, the decay order of the term that is given by the convolution of Green functions of diffusion equation and