Global Solutions Of A 2D Chemotaxis-fluid System With Gradient-dependent Flux Limitation And Superlinear Production

In this paper,we study the following chemotaxis-Navier-Stokes system with gradient-dependent flux limitation and superlinear production:n_t+u·?n=?n-?·（n F（|?c|²）?c）,c_t+u·?c=?c-c+n^m,u_t+（u·?）u+?P=?u+n?φ,and?·u=0,in a bounded and smooth domain??R²,whereφ∈W^2,∞（?）,m>1 and F satisfies|F（ξ）|≤KF·（1+ξ）^-α2with K_F>0 andα>0.It was proved that whenα>1-¹_2m,the corresponding initial-boundary value problem has a unique and globally bounded classical solution emanating from any suitably smooth initial data.This shows that the saturation effects of concentration gradient play a role of blow-up prevention in some extent.In Chapter 1,we introduce the background and development for the associated problems,and give the main results of this paper.As preliminaries,we in Chapter 2 sketch some basic inequalities,the embedding theorems and the smoothing properties of the Neumann heat semi-group.In Chapter 3,we prove our main results.