Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Xin Zhong

doi:10.3934/cpaa.2021185

Article Contents

2022, Volume 21, Issue 2: 493-515. Doi: 10.3934/cpaa.2021185

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Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Xin Zhong

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: June 2021

Early access: October 2021

Published: February 2022

This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359), the Chongqing Talent Plan for Young Topnotch Talents (No. CQYC202005074), and the Innovation Support Program for Chongqing Overseas Returnees (No. cx2020082)

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Abstract

We consider an initial boundary value problem of three-dimensional (3D) nonhomogeneous magneto-micropolar fluid equations in a bounded simply connected smooth domain with homogeneous Dirichlet boundary conditions for the velocity and micro-rotational velocity and Navier-slip boundary condition for the magnetic field. We prove the global existence and exponential decay of strong solutions provided that some smallness condition holds true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques.

Keywords:

Nonhomogeneous magneto-micropolar fluid equations,
exponential decay,
global well-posedness,
vacuum.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76D03.

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