Global bounded solution of a 3D chemotaxis-Stokes system with nonlinear doubly degenerate diffusion

Abstract

The paper considers the following chemotaxis-Stokes system with nonlinear doubly degenerate diffusion{nt+u⋅∇n=∇⋅(|∇nm|p−2∇nm)−χ∇⋅(n∇c),x∈Ω,t>0,ct+u⋅∇c=Δc−cn,x∈Ω,t>0,ut+∇P=Δu+n∇Φ,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0 in a bounded domain Ω⊂R3 with zero-flux boundary conditions and no-slip boundary condition. In this paper, we proved that global bounded weak solutions exist whenever m>1 and p≥2. It removes the restrict 8mp−8m+3p>15 and improves the result of paper Lin (2022) [15].