Global solution with partial large initial data to the Keller–Segel–Navier–Stokes equations in Besov spaces

In this paper, we prove a global large solution result to the Keller–Segel–Navier–Stokes equations in critical Besov spaces. The result indicates that the global solutions exist without any small conditions imposed on the initial oxygen concentration $c_0$ $c_{0}$ . This is different from some known large solutions results, which allow the part large initial data $u_0$ $u_{0}$ .