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, {n(t) + u . del n = Delta n - del . (n del c) + f(n), x is an element of Omega, t > 0, c(t) + u .del c = Delta c - c + n, x is an element of Omega, t > 0, u(t) = Delta u + del P + n del phi, x is an element of Omega, t > 0, del . u = 0, x is an element of Omega, t > 0. The global solvability of the system in a generalized sense is obtained under the hypothesis that the logistic source function f is an element of C-1 ([0, infinity)) as satisfies a very mild condition: f (0) >= 0 and f(s)/s -> -infinity as s -> infinity. 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.

Automated summary

This paper studies the global solvability of a two-dimensional chemotaxis-fluid model, and shows that persistent Dirac-type singularities can be ruled out without imposing any critical superlinear exponent restriction on the logistic source function.