Regularity and uniqueness for the compressible full Navier-Stokes equations

In this paper, we develop some new L-p gradient estimates of the solutions to the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting fluids in the whole space R-3. The "div-curl" decomposition technique plays an important role in deriving the key estimate parallel to del u parallel to(L)(3). As a result, we prove the existence of global solutions belonging to a new class of functions in which the uniqueness can be shown to hold, provided the initial energy is suitably small. Compared with the existing results, the lower regularity of initial data is required. (C) 2020 Elsevier Inc. All rights reserved.