Exponential Stability of Spherically Symmetric Solutions to Nonlinear Non-autonomous Compressible Navier-Stokes Equations

Abstract

This chapter is a continuation of Chapter 1 in Qin and Huang [102]. Here we establish the exponential stability of spherically symmetric solutions to an initialboundary value problem for nonlinear non-autonomous compressible Navier- Stokes equations with an external force and a heat source in bounded annular domains ${G}_{n} = \{x \in {\mathbb{R}}^{n} : 0 < a \leq |x| \leq b\} \ {\rm{in}} \ {\mathbb{R}}^{n} \ (1 \leq {n} \leq 3)$, based on the uniform estimates obtained in Chapter 1 of Qin and Huang [102].