  A compactness framework is established for approximate solutions to
subsonic-sonic flows governed by the steady full Euler equations for
compressible fluids in arbitrary dimension. The existing compactness frameworks
for the two-dimensional irrotational case do not directly apply for the steady
full Euler equations in higher dimensions. The new compactness framework we
develop applies for both non-homentropic and rotational flows. One of our main
observations is that the compactness can be achieved by using only natural weak
estimates for the mass balance and the vorticity, along with the Bernoulli law
and the entropy relation, through a more delicate analysis on the phase space.
As direct applications, we establish two existence theorems for
multidimensional subsonic-sonic full Euler flows through infinitely long
nozzles.
