Global Solutions to the Compressible Navier–Stokes Equations for a Reacting Mixture

Existence theorems are established for global generalized solutions to the compressible Navier–Stokes equations for a reacting mixture with discontinuous Arrhenius functions, which describe dynamic combustion. Equivalence of the Navier–Stokes equations in the Euler coordinates and the Lagrange coordinates for the generalized solutions is verified. The asymptotic behavior of the generalized solutions with different boundary conditions is identified and proved.