The Exponential Attractor Of Chemotaxis-fluid System

In this thesis,we study the existence of the global weak solution and exponential attractor to the coupled Chemotaxis-fluid system with the initial-boundary value.In section 1,the existence of global weak solution to the Chemotaxis-fluid system is studied.Firstly,we obtain the local existence of the weak solution to the system by using the Schauder fixed point theorem.Furthermore,we investigate the regularity estimate of this system.Utilizing the Moser-type iteration and standard parabolic regularity theory,the existence of global weak solution is obtained.In section 2,the existence of exponential attractor to the Chemotaxis-fluid system is studied.Firstly,the system is rewritten to an abstract equation.We get the local existence of weak solution to the abstract equation,and the existence of local weak solution to Chemotaxisfluid system is obtained by materializing the abstract space.Secondly,according to the energy inequalities and the regularity of local weak solution,it is proved that the system possesses a higher regularity of global weak solution.Then the semigroup of operator (?)(t) is defined by using the existence of the global weak solution.Finally,it is proved that the existence of exponential attractor is obtained for the dynamical system corresponding to the semigroup (?)(t) according to the existence theorem of exponential attractor.