| In this paper,we study the Neumann initial-boundary value problem for the following Keller-Segel(-Navier)-Stokes system with indirect signal production mechanism in a bounded domain:(?)where Ω(?)RN(N∈{2,3})is the bounded domain with a smooth boundary.The structure of this paper is as follows:The introduction introduces the background of model and research status of chemotaxis-fluid system.In chapter 1,we mainly explains the research content and main results of this paper,and gives some necessary prelimilary knowledge.In chapter 2,we study the global existence and boundedness of classical solutions of system(*)in the 2-dimensional case when the following conditions hold:the convection coefficient k=0 and the sensitivity function S(n)satisfies |S(n)|≤Cs(1+n)-α(Cs>0,α≥0).In chapter 3,we study the global existence and boundedness of classical solutions of system(*)in the 3-dimensional case when the following conditions hold:the convection coefficient k=0 and the sensitivity function S(n)satisfies |S(n)|≤Cs(1+n)-α(Cs>0,α>1/9).In chapter 4,it is proved that the classical solution of the system(*)exists globally and converges to a steady state when N ∈ {2,3},convection coefficient k≠0 and chemotactic sensitivity function S(n)≡1 under the small initial value condition. |
