Global existence of solutions without Dirac-type singularity to a chemotaxis–fluid system with arbitrary superlinear degradation

In this paper, we study a chemotaxis–fluid model in a two-dimensional setting as below, {nt+u·∇n=Δn-∇·(n∇c)+f(n),x∈Ω,t>0,ct+u·∇c=Δc-c+n,x∈Ω,t>0,ut=Δu+∇P+n∇ϕ,x∈Ω,t>0,∇·u=0,x∈Ω,t>0.The global solvability of the system in a generalized sense is obtained under the hypothesis that the logistic source function f∈ C¹([0 , ∞)) satisfies a very mild condition: f(0) ≥ 0 and f(s)s→-∞ as s→ ∞. This result exhibits that without any critical superlinear exponent restriction on f, persistent Dirac-type singularities can be ruled out in our model. This work can be regarded as a natural follow-up to the recent paper due to Winkler.