The Study On The Fluid Dynamical Equations Of Atmospheric And Oceanic Dynamics

This article mainly studied some related fluid mechanics model in the at-mosphere and ocean,mainly including oceanic and atmospheric primitive equa-tions and the interaction of fluid and particles:Flowing Regime model.This article mainly use classical energy method,Maximum principle,iterative method and other methods,and some important inequalities,such as Poincare inequali-ty,Cauchy-Schwarz inequality,Holder inequality,Young inequality,Sobolev embedding theorem and the implicit function existence theorem,etc.We study the well-posedness problem of fluid-particle model:flowing regime system and the blow-up problem of primitive equation of oceanic and atmospheric.In Chapter 1,we mainly introduces the development history of the two mod-els,research progress of preparation of knowledge and the research content in this paper.In Chapter 2,we mainly study the Cauchy problem of fluid-particle mod-el:flowing regime system in the whole space.We research that in the three-dimensional space,the local existence and uniqueness of strong solutions and we got a local classical solution through the strong solution derived.Due to the particularity of the model,we can use the method of Navier-Stokes model to study the related complex problems:Flowing Regime model.By studying the corresponding local solution of linear equations and then by using the iterative principle,then we get the to study the local solution of Flowing Regime model.Firstly,we study the corresponding linear equations,in a certain regularity of a known vector,we obtained the existence and uniqueness of the local solution of linear equations with the initial-boundary value problem.Secondly,we use the iterative method,construct a set of approximate solution,and use the energy method and some important inequalities,we get well-posedness of the solution of the three-dimensional Flowing Regime model.In Chapter 3,we mainly study the Cauchy problem of fluid-particle mod-el:flowing regime system in the whole space.We research that in the three-dimensional space,the global existence and uniqueness of strong solutions.Firstly,we find a equilibrium solution with the velocity be zero and the den-sity of particle be a constant.We make a disturbance transformation near the steady-state solution of the original model.Then we can be obtained the well-posedness of solution in a certain period of time with certain initial value and the regularity condition of the potential function.Secondly,through the analysis for the parameters and given the fit one,we get the well-posedness of the global solutions of the Flowing Regime model.In Chapter 4,we study the blow-up problem of primitive equation of oceanic and atmospheric.We mainly considers the finite-time blow up for the three-dimensional primitive equation of oceanic and atmospheric without viscous with the initial-boundary value problem of finite time,in which the unknown variables on horizontal space is periodic.By given appropriate initial value,we deduce the expression of p_xand restrict the problem on x=0,y=0.In Chapter 5,we make some preparatory work for blow-up problem of viscous primitive equation of oceanic and atmospheric.