Global smooth solutions to the two-dimensional axisymmetric Zeldovich-von Neumann-Döring combustion equations with swirl

This paper studies the two-dimensional (2D) Zeldovich-von Neumann-Döring (ZND) combustion equations with initial data, which are a combination of an axisymmetric flow in a ring and vacuum in the remaining domain. Existence of a global-in-time smooth solution to the initial value problem is obtained by the method of characteristic decomposition, provided that the initial data satisfy some sufficient conditions. The large-time behavior of the solution is also studied. As a result, at any time, the ring continues to expand until the gas burns out in infinite time for the system. The solution describes a phenomenon of the expansion of 2D reacting flows with swirl in vacuum or a phenomenon of “fire whirl”.