Global Solution And Decay Rate For A Reduced Gravity Two And A Half Layer Model

In this paper,we investigate the reduced gravity two and a half model in oceanic fluid dynamics.In a finite domain(for the initial-boundary value problem),on the one hand,we obtain the existence and uniqueness of regular solutions.On the other hand,with time t→∞,we consider a collection of the decay rate estimates for hi-(?)i(with (?)i being the stationary layer thickness)and ui(i = 1,2)in L2(Ω)-norm as well as H1(Ω)-norm.Compared with the results in[30,31],this paper utilize the BD entropy estimate with the small-ness assumption on the initial data,we can obtain the desired uniform lower and upper bounds for h1 and h2 and global a prior estimate in time.What’s more,the corresponding equations of the model have additional cross-terms,which increases the difficulty for the relevant decay rate estimates.In Chapter 1,we introduce the progress of the two and a half layer model and the theory of the compressible Navier-Stokes equations.In Chapter 2,for the initial and boundary data of the system(1.1),we consider the existence and uniqueness of regular solutions.In the Chapter 3,for the system(1.1),with time t→∞,using global a prior estimate in time,we obtain the relevant decay rate estimates.