Communications in Mathematical Sciences

Volume 22 (2024)

Number 6

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

Pages: 1549 – 1567

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n6.a5

Authors

Honghua Chen (Department of Mathematics, Shanghai University, Shanghai, China; and School of Mathematics and Statistics Science, Ludong University, Yantai, China)

Geng Lai (Department of Mathematics, Shanghai University, Shanghai, China; Newtouch Center for Mathematics, Shanghai University, Shanghai, China)

Wancheng Sheng (Department of Mathematics, Shanghai University, Shanghai, China; Newtouch Center for Mathematics, Shanghai University, Shanghai, China)

Abstract

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”.

Keywords

ZND combustion model, axial symmetric flow, characteristic decomposition, vacuum

2010 Mathematics Subject Classification

35L03, 35L60, 35L65, 35L67, 80A32

Full Text (PDF format)

The work of the first and third authors were partially supported by NSFC 12171305. The work of the second author was partially supported by NSFC 12071278 and National Science Foundation of Shanghai grant 23ZR1422100.

Received 29 May 2023

Accepted 28 December 2023

Published 18 July 2024