On The Primitive Equatious Of The Large-scale Atmosphere In The Log-pressure Coordinates

In this doctoral dissertation, we are concerned with the global existence of weak solutions, the well-posedness of strong solutions and the existence of global attractors of the following initial-boundary problems about the three dimensional viscous large-scale primitive equations in the log-pressure coordi-nates: in the domain under the following conditions: Here (x,y,z)∈Ω is coordinates, where Hs is a constant ’scale height’and p*is a constant reference pressure. We denote the boundary of Ω by where We first give the definition and properties of v and v and we divide the equa-tions with respect to v into two systems with respect to v and v in the three dimensional domains, respectively. One is the incompressible Navier-Stokes equations in the two dimensional domains, the other is the equations with re-spect to v without the pressure term. Then we give some a priori estimates about T, v, v and v, by which we prove the global existence of weak solutions, the well-posedness of strong solutions for the equations (1). At the same time, we obtain the existence of the (V, V)-and (V,(H2(Ω))3)-absorbing sets. Fi-nally, we have obtained the existence of (V,(H3(Ω))3)-absorbing sets by the elliptic regularity theory, and the existence of the (V, V)-and (V,(H2(Ω))3)-global attractors for the equations (1) by using the Sobolev compact imbedding theory.This thesis consists of four chapters.In Chapter one, the development and the study on the primitive equations of the large-scale atmosphere are introduced.In Chapter two, some preliminary results and definitions that we will used in this thesis are presented, and the equations (1) are reformulated.In Chapter three, some a priori estimates are given.In Chapter four, by means of some a priori estimates given in chapter three, we have proved the global existence of weak solutions, the well-posedness of strong solutions, the existence of (V, V)-and (V,(H2(Ω))3)-absorbing sets, and the existence of (V,(H3(Ω))3)-absorbing sets are obtained by the elliptic regularity theory. Finally, the existence of (V, V)-and (V,(H2(Ω))3)-global attractors by using the Sobolev compact embedding theory are proved.