Global well-posedness to the nonhomogeneous magneto-micropolar fluid equations with large initial data and vacuum

Xin Zhong

doi:10.3934/dcdsb.2022102

Article Contents

2023, Volume 28, Issue 2: 872-892. Doi: 10.3934/dcdsb.2022102

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Global well-posedness to the nonhomogeneous magneto-micropolar fluid equations with large initial data and vacuum

Xin Zhong

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

Received: October 31, 2021

Early access: June 2022

Published: February 2023

This research was partially supported by National Natural Science Foundation of China (Nos. 11901474, 12071359) and Exceptional Young Talents Project of Chongqing Talent (No. cstc2021ycjh-bgzxm0153)

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Abstract

We investigate global well-posedness to nonhomogeneous magneto-micropolar fluid equations with zero density at infinity in $ \mathbb{R}^2 $. We show the global existence and uniqueness of strong solutions. It should be pointed out that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies crucially upon the duality principle of BMO space and Hardy space, a lemma of Coifman-Lions-Meyer-Semmes (Coifman et al. in J Math Pures Appl 72: 247–286, 1993), and cancelation properties of the system under consideration.

Keywords:

Nonhomogeneous magneto-micropolar fluid equations,
Cauchy problem,
global well-posedness,
large initial data,
vacuum.

Mathematics Subject Classification: 35Q35, 76D03.

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