| In this thesis,we study the following three models from Keller-Segel systems:the Keller-Segel system with nonlinear sensitivitythe Keller-Segel-Navier-Stokes system with matrix-valued sensitivityas well as the attraction-repulsion Keller-Segel system Here the smooth bounded domain Ω（?）RN,a ≥2/N,S ∈ C2（（?） ×[0,∞）2)N×N,φ∈C1+δ（?）withδ∈（0,1）,x,ξ≥0,and η,β,γ,δ>0.The thesis consists of the following five chapters:In Chapter 1,we introduce the background with rich conclusions on Keller-Segel systems.In Chapter 2,we study the Keller-Segel system with nonlinear sensitivity.Under the homo-geneous Neumann boundary condition ▽n·v = ▽c·v = 0,we discuss the global boundedness of solutions,where v denotes the unit outer normal of （?）.Denote n0=1/|Ω|∫Ωn0（x）dx.We prove that for a ≥ max{1,N/1},N≥ 1,the system possesses global classical solutions decaying to the constant steady state（n0,n0）exponentially provided ||u0||Lq*（Ω）and ||▽v0||Lp*（Ω）,small enough with If a ∈（3/2,1）,N≥ 3,||n0||L2/Na（Ω）and ||▽C0||LNa（Ω）sufficiently small,then the above result still holds to the corresponding mild solutions of the system.Chapter 3 considers the Keller-Segel-Navier-Stokes system in liquid environments.LetN ∈{2,3},|S|≤Cs for some Cs>0.Under the boundary condition Vc·v =（▽n-nS（x,n,c）·▽c）·v =0,u = 0,we prove that there exists ε0>0 such that if ||n0||L2/N（Ω）,||▽co||LN（Ω）,||u0||LN（Ω）≤ε0,then the system possesses global classical solutions decaying to（n0,n0,0）exponentially.In Chapter 4,we deal with finite time blow-up on nonradial solutions to the Keller-Segel system of attraction-repulsion model under the the homogeneous Neumann boundary condition▽n·v = ▽c·v = ▽w · v = 0.For N = 2,we establish that the finite time blow-up of nonradial solutions occurs at x0 ∈Ω whenever xη-ξγ>0,the initial mass ∫Ω no（x）dx>8π/（xη-ξγ）,and ∫Ω n0（x）|x-x0|2dx sufficiently small.Chapter 5 summarizes the main results of the thesis,and proposes further problems to be studied. |
