Vortical and self-similar flows of 2D compressible Euler equations

• This paper presents the vortical and self-similar solutions for 2D compressible Euler equations.
• These solutions complement Makino’s solutions in radial symmetry without rotation.
• The rotational solutions provide further reference examples for numerical methods.
• The corresponding blowup, time-periodic or global existence conditions are classified.
• A conjecture regarding rotational solutions in 3D is made.

This paper presents the vortical and self-similar solutions for 2D compressible Euler equations using the separation method. These solutions complement Makino’s solutions in radial symmetry without rotation. The rotational solutions provide new information that furthers our understanding of ocean vortices and reference examples for numerical methods. In addition, the corresponding blowup, time-periodic or global existence conditions are classified through an analysis of the new Emden equation. A conjecture regarding rotational solutions in 3D is also made.