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

Abstract

We prove that the smooth solutions to the Cauchy problem for the Navier-Stokes equations with conserved mass, total energy and finite momentum of inertia loses 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.

14 pages, submitted

References in corpus (1)

• Generalized momenta of mass and their applications to the flow of compressible fluid

Cited by in corpus (4)

• Smooth imploding solutions for 3D compressible fluids
• Weak-strong uniqueness property for models of compressible viscous fluids near vacuum
• Non-existence of global classical solutions to barotropic compressible Navier-Stokes equations with degenerate viscosity and vacuum
• Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions