On a decay rate for 1D-viscous compressible barotropic fluid equations.
The authors study the long time behaviour of solutions to the Navier-Stokes system describing the motion of a viscous, barotropic flow in one space dimension. They show that each solution decays exponentially to a static solution provided an external force is imposed so that this (static) solution is strictly positive. One of the main (nontrivial) ingredients of the proof is a lower bound on the density field uniform in time. The results are shown for the system written in the Eulerian coordinates and for a wide class of the pressure-density state equations including the isentropic case.
scientific article; zbMATH DE number 1757488