Shock Wave Solutions of the Axisymmetric Euler Equations for Polytropic
Gases
Yuxi Zheng
Abstract
We construct entropy weak solutions to the axisymmetric and self-similar
Euler equations for gamma-law polytropic gases in two space dimensions
with all initial velocities swirling inward. We find that shock waves are
needed in the construction of the solutions.
The solutions are globally bounded, satisfy physical entropy conditions,
and have finite local energy and vorticity with well-defined initial and
boundary values.