Global Entropy Solutions to Exothermically Reacting, Compressible Euler Equations
نویسنده
چکیده
The global existence of entropy solutions is established for the compressible Euler equations for one-dimensional or plane-wave flow of an ideal gas, which undergoes a one-step exothermic chemical reaction under Arrhenius-type kinetics. We assume that the reaction rate is bounded away from zero and the total variation of the initial data is bounded by a parameter that grows arbitrarily large as the equation of state converges to that of an isothermal gas. The heat released by the reaction causes the spatial total variation of the solution to increase. However, the increase in total variation is proved to be bounded in t > 0 as a result of the uniform and exponential decay of the reactant to zero as t approaches infinity.
منابع مشابه
Global Solutions to a Model for Exothermically Reacting, Compressible Flows with Large Discontinuous Initial Data
We prove the global existence of solutions of the Navier-Stokes equations describing the dynamic combustion of a compressible, exothermically reacting fluid, and we study the large-time behavior of solutions, giving necessary and sufficient conditions for complete combustion in certain cases. The adiabatic constants and specific heats of the burned (product) and unburned (reactant) fluids may d...
متن کاملOn the Navier-stokes Equations for Exothermically Reacting Compressible Fluids
We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, includin...
متن کاملVanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions to the compressible Euler equations may blow up near the origin at certain time under some circumstance. The central feature is the strengthening of waves ...
متن کاملInitial Boundary Value Problem for Compressible Euler Equations with Relaxation
In this paper, we study the global exisitence of L∞ weak entropy solution to the initial boundary value problem for compressible Euler equations with relaxtion and the large time asymptotic behavior of the solution. Motivated by the sub-characterisitic conditions, we proposed some structural conditions on the relaxation term comparing with the pressure function. These conditions are proved to b...
متن کاملGlobal Entropy Solutions in L∞ to the Euler Equations and Euler-poisson Equations for Isothermal Fluids with Spherical Symmetry
GLOBAL ENTROPY SOLUTIONS IN L∞ TO THE EULER EQUATIONS AND EULER-POISSON EQUATIONS FOR ISOTHERMAL FLUIDS WITH SPHERICAL SYMMETRY ∗ GUI-QIANG CHEN† AND TIAN-HONG LI† Abstract. We prove the existence of global entropy solutions in L∞ to the multidimensional Euler equations and Euler-Poisson equations for compressible isothermal fluids with spherically symmetric initial data that allows vacuum and ...
متن کامل