Global Solvability to a 3D Chemotaxis-Fluid Model with Matrix-Valued Supercritical Sensitivities

In this paper, a 3D chemotaxis-fluid system which includes matrix-valued sensitivity functions and porous medium type diffusion is studied. Assuming that the matrix-valued function and diffusion term satisfy some conditions and suitably regular nonnegative initial data, the global existence of weak solutions is obtain to the system by related theories of partial differential equation and functional analysis.