Decay estimates of the 3D magneto-micropolar system with applications to L₃-strong solutions

Abstract

In this paper, we investigate the well-posedness and large time behavior of solutions to the 3D incompressible magneto-micropolar equations. By virtue of the $L_p-L_q$ estimate obtained through the spectral decomposition of the linearized magneto-micropolar equations, we show the existence and uniqueness of small $L_3$-strong solutions of the equations with small initial data. Then basing on this result, we derive sharp time decay estimates of the $L_3$-strong solutions.

Keywords:

• 3D magneto-micropolar equations
• spectral decomposition
• banach contraction mapping principle
• large time decay

Mathematics Subject Classifications:

• 35B40
• 35Q35
• 35Q30

Acknowledgments

The authors are grateful to the anonymous referees for the kind suggestions that improved this paper.

Disclosure statement

The authors do not have any relevant financial or non-financial competing interests. On behalf of all authors, the corresponding author states that there is no conflict of interest.

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.