Global strong solutions with large oscillations to the 3D full compressible Navier–Stokes equations without heat conductivity

We are concerned with the Cauchy problem to the three-dimensional full compressible Navier–Stokes equations with zero heat conductivity. Under the condition that the initial energy is small enough, global existence of strong solutions is established. Especially, the initial density is allowed to have large oscillations. The key to estimate the pointwise lower and upper bounds of the density lies in the handling of the energy conservation equation and the boundedness of the \(L^r\)–norm of the gradient of the pressure.