Existence and Uniqueness of Global Solutions of the Modified KS-CGL Equations for Flames Governed by a Sequential Reaction

Abstract

In this paper, we are concerned with the existence and uniqueness of global solutions of the modified KS-CGL equations for flames governed by a sequential reaction, where the term $|P|^2P$ is replaced with the generalized form $|P|^{2σ}P,$ see [18]. The main novelty compared with [18] in this paper is to control the norms of the first order of the solutions and extend the global well-posedness to three dimensional space.