Existence of global strong solutions for a reduced gravity two-and-a-half layer model

Abstract

In this paper, we consider the existence of global strong solutions to a reduced gravity two-and-a-half layer model in one-dimensional periodic domain. This work is inspired by Constantin-Drivas-Nguyen-Pasqualotto ((2020) [2]). Based on the Bresch-Desjardins entropy and the analysis of the evolution of the active potential, we obtain the continuation criterion and global existence of strong solutions when there is no vacuum. Due to the structure complexity of the reduced gravity two-and-a-half model, we still need to deal with the extra cross terms, which is different from Constantin-Drivas-Nguyen-Pasqualotto ((2020) [2]).