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

TL;DR

This paper investigates the decay rates and long-term behavior of solutions to the 3D magneto-micropolar fluid equations, highlighting the impact of linear damping on the decay of micro-rotational fields and their asymptotic similarity to linear solutions.

Contribution

It provides sharp decay estimates and asymptotic analysis for 3D magneto-micropolar fluids, emphasizing the role of linear damping in solution decay rates.

Findings

Micro-rotational field decays faster due to linear damping.

Solutions asymptotically approach linear solutions over time.

Derived derivative estimates of solutions may be of independent interest.

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.