Optimality of the decay estimate of solutions to the linearised curl-free compressible Navier-Stokes equations (Q6184831)

The authors consider a barotropic compressible Navier-Stokes system in three spatial dimensions for density and velocity of a barotropic fluid. The large-time behaviour of the solution to a linearised version of the above problem is examined, particularly time-decay estimates. The optimal bound on the solution of the linearised system is obtained: the upper bound in terms of time \(t\) and the spatial norm of solutions is given and proved to be sharp. The bound from below is claimed as the main result; it proves that the decay rate in \(L_\infty\) is optimal, or sharp.