Global Weak Solvability for a Chemotaxis-Fluid Model with Low Regular Initial Data

We study the initial-boundary value problem of two-dimensional Chemotaxis-fluid coupling system with logistic term This paper proves that the global existence of weak solution of system exists when the initial data are only integrable functions. More precisely, it is proved that under the assumption that r \geqslant 0,\text \mu > 0, for any \alpha \geqslant 2 and the initial value n_0 belongs to L^1(\varOmega ) , the above system admits a global weak solution.