Decay Rates for Strong Solutions to the Compressible Navier–Stokes Equations without Heat Conductivity

Abstract

In this paper, we consider the compressible Navier–Stokes equations without heat conductivity in $${\mathbb {R}}^{3}.$$ The global existence and uniqueness of strong solutions are established when the initial value towards its equilibrium is sufficiently small in $$H^{2}({\mathbb {R}}^{3}).$$ The key uniform bound of entropy is obtained, even though the entropy is non-dissipative due to the absence of heat conductivity. Moreover, the time decay rates of global solutions are also given.