Global classical solutions of the full compressible Navier–Stokes equations with cylindrical or spherical symmetry

Abstract

In this paper, we consider the full compressible Navier–Stokes equations in N(N≥2) space dimension with cylindrical or spherical symmetric initial data. The global existence of strong and classical solutions is established. The analysis is based on some delicate a priori estimates which depend on the assumption κ(θ)=θq where q⩾0 and (ρ0,θ0)∈H2,(u0,v0,w0)∈H01∩H2. Compared with the results in Wen and Zhu (2014) and Qin, Yang, Yao and Zhou (2015), our results relax the restriction q>0, when there is no initial vacuum and include the global existence of classical solutions for both the cylindrical or spherical symmetric cases, respectively. It should point out that we obtain the global classical solutions with the help of weighted H3 estimates of (u,v,w,θ).