The Attractor Of Kolmogorov-Spieqel-Sivashinsky Equation

The regularity of global attractor and the asymptotic attractor of Komogorov-Spieqel-Sivashinsky equation with periodic boundary conditions are investigated in the thesis.In the first part, it is studied that the KSS equation possesses a global attractor in Hk(?)(k > 0) by using the regularity estimates for linear operator semigroup and the iteration technique. Firstly, it is proved that the solution of the system is uniformly bounded. Secondly,the existence of the absorbing set in Hk(?)(k>0) is obtained.In the second part, the asymptotic attractor of KSS equation in L2(?) and the dimensional estimate of asymptotic attractor are studied. Firstly, the solution sequence is constructed by using orthogonal decomposition. Secondly, it is proved that the solution sequence converges to the solution of the equation by two processes.