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On the Navier-Stokes Equations for Exothermically Reacting
Compressible Fluids

#### Author: Gui-Qiang Chen, David Hoff, and Konstantina Trivisa

#### Title: On the Navier-Stokes Equations for Exothermically Reacting
Compressible Fluids

**Abstract**
We analyze mathematical models governing planar flow of chemical reaction
from {\em unburnt gases} to {\em 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, including stability,
regularity, and large-time behavior, of global discontinuous solutions
of large oscillation to the Navier-Stokes equations with constant
adiabatic exponent $\gamma$ and specific heat $c_v$.
Our approach for the existence and regularity is to combine the
difference approximation techniques with the energy methods,
total variation estimates, and weak convergence arguments to
deal with large jump discontinuities;
and for large-time behavior is an a posteriori argument directly
from the weak form of the equations.
The approach and ideas we develop here can be applied to solving
a more complicated model where $\gamma$ and $c_v$ vary as the phase
changes; and we then describe this model in detail and contrast
the results on the asymptotic behavior of the solutions
of these two different models.
We also discuss other physical models describing dynamic combustion.

This article has appeared in:

* Acta Mathematicae Applicatae Sinica, English Series *,
**vol. 18 (1)**, pages 15-36 (2002)

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A closely related paper is Change me.

**Author Address**
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu