In this work the close relation between vorticity and micro-rotation in micropolar flows in Rn (n = 2 or 3) is identified and used to explain the faster decay by t^(-1/2) of the angular velocity of the micro-rotation of fluid particles, as well as establishing its optimality. For this purpose important upper and lower bounds for Leray solutions in homogeneous Sobolev spaces are derived, using the monotonicity approach recently introduced by the authors for dissipative systems in general. Several related results of interest are also given along the discussion.

The spontaneous synchronization between micro-rotation and vorticity in micropolar flows in R n (n = 2, 3) is investigated and used to explain the faster decay by t −1/2 of the angular velocity of the fluid particles' microrotation, as well as establishing its optimality. This synchronization effect remained elusive for sixty years of investigations in micropolar fluid flows and was revealed after important upper and lower bounds for the solutions in Ḣm (R n ) were obtained by the authors, using the monotonicity approach for general dissipative systems introduced in [22]. Several related results of independent interest are also given along the discussion.