Minea System The Long Time Behavior Of The Finite Difference Scheme

In this paper, Minea system is considered, which is a kind of simplify of Navier-Stokes system. The existence of an attractor is one of the most important characteristics for a dissipative system. The long-time dynamics is completely determined by the attrac-tors of the system.At first, introduction, domestic and international research results of Navier-Stokes system are introduced. Because the equations is one of nolinear ODES, and it is impossible to obtain the solutions. We have to study the numerical computing methods. In chapter two, a backward Euler difference scheme and a Crank-Nicolson difference scheme are given for the transformed equations. The local truncation errors of the difference schemes are first order accurate and second order accurate respectively. The existence of the difference solution is proved by fixed point theorem. In chapter four and five, the stability and convergence of the two schemes are obtained. Finally, in chapter six, the long time behavior of the two difference schemes are discussed. The existence of absorbing sets and global attractors of the dynamic system which generated by the two difference shemes are proved. In chapter seven, two examples of numerical simulation are given.