Partial regularity and L3 -norm concentration effects around possible blow-up points for the micropolar fluid equations
Résumé
The micropolar fluid system is a model based on the Navier-Stokes equations which considers two coupled variables: the velocity field $\vu$ and the microrotation field $\vw$. Assuming an additional condition over the variable $\vu$ we will first prove that weak solutions $(\vu, \vw)$ of this system are smooth. Then, we will present a concentration effect of the $L^3_x$ norm of the velocity field $\vu$ near a possible singular time.
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