  The combustion model is studied in three-dimensional (3D) smooth bounded
domains with various types of boundary conditions. The global existence and
uniqueness of strong solutions are obtained under the smallness of the gradient
of initial velocity in some precise sense. Using the energy method with the
estimates of boundary integrals, we obtain the a priori bounds of the density
and velocity field. Finally, we establish the blowup criterion for the 3D
combustion system.
