Communications in Mathematical Sciences

Volume 17 (2019)

Number 4

Optimal decay rates of the compressible magneto–micropolar fluids system in $\mathbb{R}^3$

Pages: 1109 – 1134

DOI: https://dx.doi.org/10.4310/CMS.2019.v17.n4.a13

Authors

Leilei Tong (Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing, China)

Zhong Tan (School of Mathematical Sciences and the Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Xiamen, China)

Abstract

In this paper, we consider the Cauchy problem of the compressible magneto–micropolar fluids system in $\mathbb{R}^3$ with initial data close to some constant steady state. Based on the spectral analysis on the semigroup generated by the linearized equations and the nonlinear energy estimates, we show that the solution of the magneto–micropolar fluids system converges to its constant equilibrium state at the exact same $L^2$-decay rate as the linearized equations, which shows that the convergence rate is optimal.

Keywords

lower convergence rates, upper decay rates, spectral analysis, energy method

2010 Mathematics Subject Classification

35B40, 35D35, 35Q35, 76N10

Full Text (PDF format)

The research for this paper was supported by the Chongqing University of Posts and Telecommunications startup fund (Grant No. A2018-128), and by the National Natural Science Foundation of China (Grant Nos. 11271305, 11531010).

Received 27 October 2018

Accepted 1 June 2019

Published 25 October 2019