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arXiv · 2406.03291

Partial regularity and $L^3$-norm concentration effects around possible blow-up points for the micropolar fluid equations

Diego Chamorro·David Llerena
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Abstract

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

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Diego Chamorro, David Llerena. 2024-06-05. Partial regularity and $L^3$-norm concentration effects around possible blow-up points for the micropolar fluid equations. https://arxiv.org/abs/2406.03291

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