Global Stability of Steady Transonic Euler Shocks in Quasi-One-Dimensional Nozzles

TL;DR

This paper proves the global stability of steady transonic shock solutions in quasi-one-dimensional nozzles without smallness assumptions, using energy estimates and advanced analytical methods.

Contribution

It establishes the first comprehensive proof of global stability for transonic shocks in nozzles without restrictive assumptions.

Findings

Transonic shocks are globally stable in the studied setting.

Energy estimates demonstrate exponential decay of perturbations.

The approach extends previous methods to more general conditions.

Abstract

We prove global in time dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. We assume neither the smallness of the relative slope of the nozzle nor the weakness of the shock. Key ingredients of the proof are an exponentially decaying energy estimate for a linearized problem together with methods from \cite{LRXX}.