Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations
The paper addresses the question of global (in time) existence of a solution to the Navier-Stokes equation, for a barotropic (compressible) fluid, on a one-dimensional bounded domain. The authors show that this problem has a global solution if the external force is time independent, moreover they show that the density is bounded away from zero below and bounded above provided that the external force and pressure satisfy a certain compatibility condition. This compatibility condition holds if the external force is sufficiently small. If this compatibility condition does not hold the density becomes zero or infinite asymptotically.
scientific article; zbMATH DE number 4125948