Stabilization effect of temperature on three-dimensional inviscid compressible fluid

This paper solves the stability problem for a three-dimensional inviscid non-isentropic compressible fluid with radial symmetrical data in $H^4\left(R^3\right)$. We establish the stability for the nonlinear system and derive precise large-time behavior of the solutions. The result presented in this paper reveals a remarkable phenomenon for the inviscid non-isentropic compressible fluids. That is, the temperature actually smooths and stabilizes the irrotational flows. If the temperature were not present, the fluid is governed by the 3D compressible Euler equations and its stability remains open. It is the coupling and interaction between the temperature and the velocity in the inviscid system that makes the stability problem studied here possible. Mathematically the system can be reduced to degenerate and damped wave equations that fuel the stabilization.