Global Existence Of Almost Energy Solution To The Two-Dimensional Chemotaxis-Navier-Stokes Equations With Partial Diffusion

In this paper, we study Cauchy problem of the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Taking advantage of a coupling structure of the equations and using the damping effect of the growth term g(n), we obtain the necessary estimates of solution (n, c, u) without the diffusion term Delta n. These uniform estimates enable us to establish the global-in-time existence of almost weak solutions for the system.