The region between two vertical parallel glass plates is filled with fuel.
A reaction is initiated whose combustion product is lighter than the fuel.
I'll informally present some stability results for Jingyi Zhu's Hele-Shaw
model for the evolution of a boundary curve of the reaction region. The
normal velocity is the sum of the combustion effect depending on the
curvature of the curve plus the nonlocal buouyancy effect due to pressure.
This model admits a simple treatment, viewing the evolution as a
perturbation of curvature flow.