Global strong solutions and decay to the 3D full compressible Navier–Stokes equations without heat conductivity

This paper is concerned with the 3D full compressible Naiver-Stokes equations without heat conductivity in bounded domains. For the case when the velocity admits slip boundary condition, global existence and decay rate of strong solutions are established by making full use of the estimate of the gradient of pressure. Compared to previous results in $ H^s $ framework, we only need the initial velocity and pressure to be small in some sense, which indicates that the initial density can contain large oscillations. Moreover, the exponential decay rate of the velocity and pressure are obtained. It should be emphasized that the $ L^2 $–norms of $ {\rm curl} u $ and $ {\rm div}u $ are estimated separately, which shows that $ {\rm curl} u $ decays slower than $ {\rm div}u $ in $ L^2 $ under the condition that the diameter of the domain is suitably large.