Abstract
In Ω⊂Rn 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 Lp-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.
Original language | English (US) |
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Pages (from-to) | 1025-1032 |
Number of pages | 8 |
Journal | Communications in Mathematical Sciences |
Volume | 13 |
Issue number | 4 |
DOIs | |
State | Published - 2015 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics