Well-posedness for the one-dimensional inviscid Cattaneo-Christov system

Abstract

This paper is devoted to studying the inviscid compressible Cattaneo-Christov system in one-dimensional space. The iterative method will be used to establish the local well-posedness of this system for large data in critical Besov spaces based on the L2 framework. Moreover, by using the renormalized energy method, one can prove the global existence of a strong solution when the initial perturbation around a constant state is sufficiently small.