LAUSR

Abstract In this paper, a chemotaxis-Stokes system with slow p-Laplacian diffusion { n t + u ⋅ ∇ n = ∇ ⋅ ( | ∇ n | p − 2 ∇ n ) − ∇ ⋅ ( n ∇ c ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − n c , x ∈ Ω , t > 0 , u t = Δ u + ∇ P + n ∇ Φ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 , is considered under homogeneous boundary conditions of Neumann type for n and c, and of Dirichlet type for u, where Ω is a smooth bounded domain in R 3 and Φ ∈ W 2 , ∞ ( Ω ) is a given function. It is proved that global bounded weak solutions exist whenever p > 23 11 .