Global existence and large-time behavior of spherically symmetric solutions for a viscous heat-conducting ionized gas in exterior domains

Abstract

We study global-in-time spherically symmetric solutions for a viscous, compressible, heat-conducting ionized gas in a n-dimensional unbounded exterior domain with large initial data, where n ≥  2 is the space dimension. The properties of ionized gases, combined with the unboundedness of the exterior domain, make it challenging to estimate the first-order spatial derivatives of the bulk velocity and the absolute temperature. For a class of constant non-vacuum equilibrium states, we obtain the uniform-in-time bounds on the dissipative estimates for both the bulk velocity and the absolute temperature. Based on such estimates, we establish the global existence and asymptotic behavior of spherically symmetric solutions to the viscous and heat-conducting ionized gas in unbounded exterior domains with large initial data. The key point lies in deducing the lower and upper bounds on the specific volume and the temperature.