Global Solutions Of A 2D Chemotaxis-fluid System For Coral Fertilization With Gradient-dependent Flux Limitation

In this paper,we study the following Keller-Segel-(Navier-)Stokes system for coral fertil-ization with gradient-dependent flux limitation:n_t+u·?n=?n-?·(nF(|?c|²)?c)-nm,c_t+u·?c=?c-c+m,m_t+u·?m=?m-nm,u_t+?(u·?)u+?P=?u+(n+m)??,and ?·u=0,in a bounded and smooth domain ?(?)R²,where??R,??W^2,?(?),and F satisfies|F(?)|?K_F·(1+?)^-(?/2) with K_F>0 and ??R.It was proved that when ?=0,the corresponding initial-boundary problem admits a unique globally bounded classical solution for any ??R.As for ??0,the global boundedness of solutions was ascertained in the case of ??0;whereas if ?<0,the solution was shown to be global but not necessarily uniformly bounded in time.In Chapter 1,we introduce the background and development of the associated model,and give the main results of this paper.As preliminaries,we in Chapter 2 sketch some basic inequal-ities,the smoothing estimates of the Neumann heat semigroup and the fundamental properties of fractional operator.In Chapter 3,we prove our main results.