Global bounded weak solution for a 3D chemotaxis-Stokes system with slow [formula omitted]-Laplacian diffusion and rotation

Abstract

In this paper, we consider the chemotaxis-Stokes system with p-Laplacian (p>2)nt+u⋅∇n=∇⋅(|∇n|p−2∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut+∇P=Δu+n∇ϕ+f(x,t),∇⋅u=0 in a smooth bounded domain Ω∈R3 with zero-flux boundary conditions and no-slip boundary condition, where S(x,n,c) satisfies S∈C2Ω̄×[0,∞)2;R3×3 and |S(x,n,c)|≤S0c(1+n)−α for all (x,n,c)∈Ω×[0,∞)2 with α≥0 and some nondecreasing function S0:[0,∞)→[0,∞). It is shown that there exists a global bounded weak solution when 43p+α>259, which removes the restriction 11p+6α+2pα>23 and improves the result of paper (Zhuang et al., 2020).