We consider a one-dimensional compressible Navier-Stokes model for reacting gas mixtures with the same γ-law in dynamic combustion. The unknowns of the PDE system consist of the inverse density, velocity, temperature, and mass fraction of the reactant (Z). First, we show that the graph of Z cannot form cusps or corners near the points where the reactant in the combustion process is completely depleted at any time, based on a Bernis-type inequality by M. Winkler (2012) and the recent works by T. Cieślak et al (2023). In addition, we establish the global well-posedness theory of small BV weak solutions for initial data that are small perturbations around the constant equilibrium state (1, 0, 1, 0) in the L¹(R)∩BV(R)-norm, via an analysis of the Green's function of the linearised system. The large-time behaviour of the global BV weak solutions is also characterised. This is motivated by and extends the recent global well-posedness theory for BV weak solutions to the one-dimensional isentropic Navier-Stokes and Navier-Stokes-Fourier systems developed by T. Liu and S.-H. Yu (2022).

*Joint with Prof. Haitao Wang and Miss Jianing Yang (SJTU)