Trajectory Attractor Of A3D Non-newtonian Fluid Equations

This thesis mainly studies the trajectory asymptotic behavior ofan incompressible non-Newtonian fluid in3D bounded domains. Thepaper is organized as follows.In chapter1, we recall the origin of the infinite dimensional dynami-cal system and introduce the physical background of the non-Newtonianfluid, as well as the issues we will study in this thesis.In chapter2, we investigate the existence of the trajectory attractorfor the3D autonomous incompressible non-Newtonian fluid. We firstconstruct the trajectory space which consists of all the weak solutionssatisfying some conditions of the non-Newtonian fluid and introduce thetranslation semigroup acting on it. Then we prove that the translationsemigroup possesses a bounded trajectory absorbing set in trajectoryspace. Further, we establish the closedness of the trajectory space andthe compactness of the trajectory absorbing set in suitable topologicalspace, respectively.In Chapter3, we verify the trajectory asymptotic behavior of the3D non-autonomous incompressible non-Newtonian fluid. Firstly, weprove the existence of the uniform trajectory attractor AΣin spaceF+loc, as well the existence of the uniform trajectory attractor UΣ(calledthe uniform regular trajectory attractor)in space M+loc(possessing moreregularity). Then we establish the regularity of the uniform trajectoryattractor by showing that AΣ=UΣ.In the last chapter, we give some conclusions and remarks.