On the Navier-Stokes equations for exothermically reacting compressible fluids
The authors study mathematical models governing plane flows with chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. They establish the existence of solutions and examine their dynamic behavior, including stability, regularity, and large-time behavior of discontinuous solutions to Navier-Stokes equations, in Lagrangian coordinates, for one-dimensional reacting compressible fluids with discontinuous initial data with large oscillations. The authors construct semidiscrete difference approximations and obtain energy and regularity estimates for approximate solutions. The a priori bounds derived show that the solutions exist globally in time, and provide sufficient compactness both to extract limiting solutions and to determine their asymptotic behavior. The difference approximation techniques by energy methods, total variation estimates, and weak convergence deal with large jump discontinuities.
scientific article; zbMATH DE number 1784811
scientific article