The Trajectory Attractor Of Brinkman-Forchheimer Equations

This thesis studies three issues of the trajectory attractor for the convective Brinkman-Forchheimer equations. The thesis consists of five chapters.In Chapter1, we first recall the origin of the infinite-dimensional dynamical system and then introduce the issue addressed in the present thesis.In Chapter2, we study the existence of the trajectory attractor for the equations. We first illustrate the existence of the solution. Then we prove that there exists trajectory absorbing set. Further we establish that the set is bounded and compact, and thus we obtain the existence of the trajectory attractor.In Chapter3, we investigate the convergence of the trajectory attractor of the equations to that of the trajectory attractor of the Navier-Stokes equations. Firstly, we prove the convergence of the so-lution of the equations to the solution of the Navier-Stokes equations. Then we prove Aαtrâ†'A0tr in the topological space (?)+loc as αâ†'0+.In Chapter4, we verify the approximation of the trajectory at-tractor by the trajectory attractor of Galerkin system for the equa-tions.In Chapter5, we summarize the thesis briefly.