Existence Of Global Strong Solutions For Periodic Problem To The One-dimensional Reduced Gravity Two-and-a-half Layer Model

In this paper,we consider the existence of global strong solutions to the reduced gravity two-and-a-half layer model in one-dimensional periodic domain.First,using the classic iterative method to prove the local existence of the strong solutions.Then based on the basic energy estimation,Bresch-Desjardins entropy estimation and the analysis of the evolution of the active potentials w_i(i=1,2),we obtain the continuation criterion and global existence of strong solutions when there is no vacuum.Compared with the article Constantin-Drivas-Nguyen-Pasqualotto[Ann.Inst.H.Poincar’e Anal.Non Lin’eaire,2020,37(1):145-180],due to the structural complexity of the reduced gravity two-and-a-half-layer model,we need to deal with cross terms in the momentum equations.The article is introduced by the following three parts:In Chapter 1,we introduce the physical background about the reduced gravity two-and-a-half layer model and the well-posed results of solutions,and well-posed results for the associated model compressible Navier-Stokes equations,and then state the main theorems of this paper;In Chapter 2,constructing the iterative sequences by linearizing the equa-tions,applying inductive and energy methods,we verify that the existence and uniqueness of the local strong solutions.Then combining basic energy estima-tion,Bresch-Desjardins entropy estimation and the analysis of the evolution of the active potentials to obtain the continuation criterion of the strong solutions;In Chapter 3,we prove the global existence of strong solutions in the case of large initial values.