Partial regularity and L³-norm concentration effects around possible blow-up points for the micropolar fluid equations

The micropolar fluid system is a model based on the Navier-Stokes equations which considers two coupled variables: the velocity field u and the microrotation field ω. Assuming an additional condition over the variable u we will first prove that weak solutions ( u, ω) of this system are smooth. Then, we will present a concentration effect of the L³ₓ norm of the velocity field u near a possible singular time.