Abstract
In this paper, we develop some new Lp gradient estimates of the solutions to the full Navier-Stokes equations for three-dimensional compressible viscous heat-conducting fluids in the whole space R3. The “div-curl” decomposition technique plays an important role in deriving the key estimate ‖∇u‖L3. 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.
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