<p>In this paper, we consider the Cauchy problem and the vacuum free boundary problem of the three-dimensional non-isentropic compressible Euler equations with spherical symmetry and cylindrical symmetry, respectively. By using some ansatzes, we construct some self-similar analytical solutions with the initial specific entropy of the form <i>S</i>₀(<i>r</i>) = <i>b</i>₀<i>r</i>, where <i>b</i>₀ is a constant. Moreover, we investigate the global existence and blowup of the constructed solutions and study the spreading rate of the free boundary for the vacuum free boundary problem by using the averaged quantities method. Finally, we provide some analytical solutions for the non-isentropic compressible Euler equations with Coriolis force. We find that the rotation can suppress the formation of singularity for the Cauchy problem and prevent the free boundary from spreading out infinitely for the free boundary problem.</p>