The Exponential Attractor Of Chemotaxis Navier-Stokes System

The global solution and exponential attractor of the chemotaxis Navier-Stokes system are investigated in this thesis.In section 1,the three existence theorems of local solution are obtained in the specific space by the local existence lemma of abstract space.In section 2,the existence of global solution for the chemotaxis Navier-Stokes system is obtained by energy methods.In section 3,the existence of exponential attractor for the chemotaxis Navier-Stokes sys-tem is studied.Firstly,the semigroup of operators is defined by the global solution.Secondly,the existence of compact absorption set is obtained for the dynamical system corresponding to the semigroup.Finally,it is proved that the system(?)possesses an exponential attractor by Lipschitz conditions.