This paper deals with asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows in the whole space $R^2$. Based on the spectral decomposition of linearized micropolar fluid flows, the sharp algebraic time decay estimates of the micropolar fluid flows in $L_2$ and $L_\infty$ norms are obtained.

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

This article examines particle dynamics and acceleration in the magnetic Penrose process (MPP) around Kerr black hole (BH) in a split monopole magnetic field. The characteristics of charged particle motion around magnetized BHs reveal four differen feasible regimes of ionized Keplerian disk behaviour: survival in regular epicyclic motion; changing into a chaotic toroidal state; collapse due to escaping along magnetic field lines and collapse due to falling into the BHs. By making use of the effective potential, we have investigated the position of stable circular orbits for both in- and off-equatorial planes. We observed that the positive magnetic field $${{\mathcal {P}}}>0$$P > 0 increases the stability of effective potential, whereas $${{\mathcal {P}}}<0$$P < 0 diminishes its stability. We show that ultra-efficient energy extraction from spinning supermassive BH controlled by the MPP can pay the bill. We anticipate neutral particle ionization, such as neutron beta-decay, edging closer to the BH horizon, charging protons to more than $$10^{20}$$10 20 eV for a supermassive BH of mass $$10^9M_{\odot }$$10 9 M ⊙ and a magnetic field of strength $$10^4$$10 4 G.