Global Well-Posedness and Optimal Time Decay Rates for the Compressible Oldroyd-B Model in $${\mathbb {R}}^2$$
Global Well-Posedness and Optimal Time Decay Rates for the Compressible Oldroyd-B Model in $${\mathbb {R}}^2$$
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DOI：
10.1007/s10884-023-10292-0
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发表时间：
2023-08
影响因子：
1.3
通讯作者：
Yuhui Chen;Minling Li;Qinghe Yao;Z. Yao
中科院分区：
文献类型：
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作者：
Yuhui Chen;Minling Li;Qinghe Yao;Z. Yao
本文研究了二维可压缩Oldrophil-B模型的整体适定性和最优时间衰减率。通过引入新的扰动量，我们找到了另一个更好的扰动系统，可以很容易地消除交叉线性项，并在框架内建立了小初始数据下强解的全局适定性。此外，在初始数据的低频有界的唯一假设下，通过使用辅助对数衰减估计和分析解的低频-高频的更精确的衰减估计，我们得到了解本身及其所有导数（包括最高空间导数）的最优时间衰减率.此外，我们对待的情况下，在不同的方式.为了证明这些结果，我们将使用时间加权能量估计，傅立叶时间分裂和半群方法。
This paper is devoted to the global well-posedness and the optimal time decay rates for the two-dimensional compressible Oldroyd-B model. By introducing new quantities, we find another better perturbation system to eliminate the cross linear terms easily and build the global well-posedness of the strong solution with small initial data in-framework. In addition, under the only assumption that the low frequency of the initial data is bounded inwith, we obtain the optimal time decay rates of the solution itself and all its derivatives (including the highest spatial derivatives) by using the auxiliary logarithmic decay estimates and analyzing the more accurate decay estimates for the low-high frequency of the solution. Moreover, we treat the casesandin a different way. To prove these results, we shall use the time-weighted energy estimate, Fourier time-splitting and semigroup methods.