Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids

Abstract

We characterize the $L^2$ decay rate of solutions to the 3D magneto-micropolar system in terms of the decay character of the initial datum. Due to a linear damping term, the micro-rotational field has a faster decay rate. We also address the asymptotic behaviour of solutions by comparing them to solutions to the linear part. As a result of the linear damping, the difference between the micro-rotational field and its linear part also decays faster. As part of the proofs of these results, we prove estimates for the derivatives of solutions which might be of independent interest.