  We investigate the 2D combustion model with Dirichlet boundary conditions and
slip boundary conditions in bounded domains. The global existence of weak and
strong solutions and the uniqueness of strong solutions are obtained provided
the initial density is small in some precise sense. Using the energy method and
the estimates of boundary integrals, we obtain the a priori bounds if the
density and velocity field. In addition, we prove the local existence of the
strong solutions via iterative method and the contraction mapping theorem.
Finally, we extend the well known Serrion's blowup criterion to the 2D
combustion model. Under the suitable boundary conditions, the Serrin's
condition on the velocity can be removed in this criteria.

Analysis of PDEs