Singularity formation to the nonhomogeneous magneto-micropolar fluid equations

Xin Zhong

doi:10.3934/dcdsb.2021021

Article Contents

2021, Volume 26, Issue 12: 6339-6357. Doi: 10.3934/dcdsb.2021021 open access

This issue Previous Article Limiting behavior of unstable manifolds for spdes in varying phase spaces Next Article Uniform stabilization of 1-D Schrödinger equation with internal difference-type control

Singularity formation to the nonhomogeneous magneto-micropolar fluid equations

Xin Zhong

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

Received: August 2020

Revised: November 2020

Early access: January 2021

Published: December 2021

This research was partially supported by National Natural Science Foundation of China (No. 11901474) and the Innovation Support Program for Chongqing Overseas Returnees (No. cx2020082)

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Abstract

We consider the Cauchy problem of nonhomogeneous magneto-micropolar fluid equations with zero density at infinity in the entire space $ \mathbb{R}^2 $. We show that for the initial density allowing vacuum, the strong solution exists globally if a weighted density is bounded from above. It should be noted that our blow-up criterion is independent of micro-rotational velocity and magnetic field.

Keywords:

nonhomogeneous magneto-micropolar fluid equations,
strong solutions,
Cauchy problem,
singularity formation.

Mathematics Subject Classification: 35Q35, 35B65.

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