Helically symmetric solutions to the 3-D Navier–Stokes equations for compressible isentropic fluids

Abstract

We prove the existence of global weak solutions to the Navier–Stokes equations for compressible isentropic fluids for any γ > 1 when the Cauchy data are helically symmetric, where the constant γ is the specific heat ratio. Moreover, a new integrability estimate of the density in any neighborhood of the symmetry axis (the singularity axis) is obtained.