Stability of periodic transonic flows in general divergent nozzles

Establish the dynamical stability of time-periodic transonic flows in a general nozzle beyond the nozzle geometry and small-expansion-rate restrictions imposed in the paper.

Background

The paper proves existence, uniqueness, and dynamical stability of small time-periodic strong transonic shock solutions for the quasi-one-dimensional full compressible Euler equations in divergent nozzles. The analysis relies on structural dissipation at the shock and on the smallness condition imposed through equation (a11), which controls the nozzle expansion rate relative to the background Bernoulli constant.

The authors explicitly state that their result does not cover periodic transonic flows in a general nozzle. Extending the stability theory to such nozzle geometries is therefore identified as an unresolved problem.