Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations

摘要

We prove that the smooth solutions to the Cauchy problem for the Navier-Stokes equations with conserved total mass, finite total energy and finite momentum of inertia lose the initial smoothness within a finite time in the case of space of dimension 3 or greater even if the initial data are not compactly supported. The cases of isentropic and incompressible fluids are also considered. (C) 2008 Elsevier Inc. All rights reserved.