Global existence and long-term stability of spherically symmetric compressible micropolar real gas flows

Abstract

We study a three-dimensional, spherically symmetric model of compressible flow for a real micropolar gas confined between two concentric spheres. The model is a generalization of the classical fluid model, whereby temperature is included and microeffects are added in terms of microrotation and the law of conservation of angular momentum. Also, a generalized equation of state for pressure is used. The spherical symmetry assumption provides a simplification in terms of analysis but still serves as a valuable modeling asset for real-world applications. Incorporating microstructural effects and non-ideal gas behavior, we prove the global-in-time existence of generalized solutions and analyze their long-term stabilization around a stationary state. The proof technique is based on estimating the solution independently of time. Our results extend previous work on ideal and micropolar gas flows by unifying these effects in a single framework and adapting proof techniques to handle the combined complexities of spherical symmetry, micropolarity, and real gas thermodynamics.