Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

Shuai Liu; Yuzhu Wang

doi:10.3934/eect.2021041

Article Contents

2022, Volume 11, Issue 4: 1201-1227. Doi: 10.3934/eect.2021041

This issue Previous Article New criteria for exponential stability in mean square of stochastic functional differential equations with infinite delay Next Article Well-posed control problems related to second-order differential inclusions

Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

Shuai Liu and
Yuzhu Wang^,

School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

^* Corresponding author: Yuzhu Wang
^* Corresponding author: Yuzhu Wang

Received: March 31, 2021

Revised: May 31, 2021

Early access: August 2021

Published: August 2022

This work was supported in part by the NNSF of China (Grant No. 11871212) and the Basic Research Project of Key Scientific Research Project Plan of Universities in Henan Province(Grant No. 20ZX002)

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Abstract

In this paper, we investigate the optimal time-decay rates of global classical solutions for the compressible Oldroyd-B model in $ \mathbb{R}^n(n = 2,3) $. Global classical solutions in two space dimensions are still open. We first complete the proof of global classical solutions in two space dimensions. Based on global classical solutions and Fourier spectrum analysis, we obtain the optimal time-decay rates of global classical solutions in two and three space dimensions. More precisely, if the initial data belong to $ L^1 $, the optimal time-decay rate of solutions and time-decay rates of $ l(l = 1,\cdot\cdot\cdot,m) $ order derivatives under additional assumptions are established.

Keywords:

Generalized compressible Oldroyd-B model,
global classical solutions,
optimal time-decay rate.

Mathematics Subject Classification: Primary: 35Q35; Secondary: 76A05.

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