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We establish the global-in-time existence of solutions of the Cauchy problemfor the full Navier-Stokes equations for compressible heat-conducting flow inmultidimensions with initial data that are large, discontinuous, sphericallysymmetric, and away from the vacuum. The solutions obtained here are of globalfinite total relative-energy including the origin, while cavitation may occuras balls centred at the origin of symmetry for which the interfaces between thefluid and the vacuum must be upper semi-continuous in space-time in theEulerian coordinates. On any region strictly away from the possible vacuum, thevelocity and specific internal energy are H\"older continuous, and the densityhas a uniform upper bound. To achieve these, our main strategy is to regard theCauchy problem as the limit of a series of carefully designed initial-boundaryvalue problems that are formulated in finite annular regions. For suchapproximation problems, we can derive uniform {\it a-priori} estimates that areindependent of both the inner and outer radii of the annuli considered in thespherically symmetric Lagrangian coordinates. The entropy inequality isrecovered after taking the limit of the outer radius to infinity by usingMazur's lemma and the convexity of the entropy function, which is required forthe limit of the inner radius tending to zero. Then the global weak solutionsof the original problem are attained via careful compactness arguments appliedto the approximate solutions in the Eulerian coordinates.

Global Spherically Symmetric Solutions of the Multidimensional Full Compressible Navier-Stokes Equations with Large Data