On the explosion problem in a ball
Alexei Novikov · Communications in Mathematical Sciences · 2015
In Ω ⊂ R n we consider the explosion problem in an incompressible flow introduced in [L.Kagan, H. Berestycki, G. Joulin, and G. Sivashinsky, Comb.Theory Model., 1, 97-111, 1997].If Ω is a ball, we show that the explosion threshold can only be increased by addition of an incompressible flow.Further, for any Ω we give a new proof of the L p -L ∞ estimate for elliptic advection-diffusion problems obtained in [H.Berestycki, A. Kiselev, A. Novikov, and L. Ryzhik, J. Anal.Math., 110, 31-65, 2010].Our proof provides an optimal estimate when Ω is a ball.