  We consider the explosion problem in an incompressible flow introduced in the
paper of H. Berestycki, L. Kagan, G. Joulin and G. Sivashinsky. We use a novel
$L^p-L^\infty$ estimate for elliptic advection-diffusion problems to show that
the explosion threshold obeys a positive lower bound which is uniform in the
advecting flow. We also identify the flows for which the explosion threshold
tends to infinity as their amplitude grows and obtain an effective description
of the explosion threshold in the strong flow asymptotics in a two-dimensional
one-cell flow.
