Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

Haibo Cui; Haiyan Yin

doi:10.3934/dcdsb.2020210

Article Contents

2021, Volume 26, Issue 6: 2899-2920. Doi: 10.3934/dcdsb.2020210

This issue Previous Article Variational solutions of stochastic partial differential equations with cylindrical Lévy noise Next Article Periodic solutions to non-autonomous evolution equations with multi-delays

Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

Haibo Cui and
Haiyan Yin^,

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

^* Corresponding author: Haiyan Yin
^* Corresponding author: Haiyan Yin

Received: March 2020

Revised: May 2020

Early access: July 2020

Published: June 2021

The authors were supported by the National Natural Science Foundation of China(Grant Nos. #11601164, #11601165 and #11971183), the Natural Science Foundation of Fujian Province of China(Grant No. 2017J05007), and the Fundamental Research Funds for the Central Universities(Grant No. ZQN-701), Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant No. ZQN-PY602)

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Abstract

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line $ \mathbb{R}_{+}: = (0, \infty). $ We mainly investigate the unique existence, the asymptotic stability and convergence rates of stationary solutions to the outflow problem for this model. We obtain the convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method by taking into account the effect of the microrotational velocity on the viscous compressible fluid.

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Mathematics Subject Classification: Primary: 34K21, 35B35, 35Q35.

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