A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum

In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of $L_t^{\mathrm{\infty }}{L}_x^q$ $L_{t}^{\infty }L_{x}^{q}$ of the density, where $1<q<\mathrm{\infty }$ $1< q<\infty $ , and it is independent on the velocity of rotation of the microscopic particles.