This paper is concerned with the study of the Cauchy problem to a multi-dimensional P1-approximation model. Based on a known global well-posedness (Danchin and Ducomet in J Evol Equ 14:155–195, 2014), in $$L^{2}$$ L 2 -critical regularity framework the time decay rates of the constructed global strong solutions are obtained if the low frequencies of the data under a suitable additional condition. The proof mainly relies on an application of Fourier analysis to a mixed parabolic-hyperbolic system, and on a refined time-weighted energy functional. As a by-product, those time-decay rates of $$L^{q}$$ L q – $$L^{r}$$ L r type are also captured in the critical framework.

中文翻译：

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辐射流体力学中 P1 近似的强解的大时间行为

本文主要研究多维 P1 逼近模型的柯西问题。基于已知的全局适定性（Danchin 和 Ducomet in J Evol Equ 14:155–195, 2014），在 $$L^{2}$$ L 2 -critical 规律框架中构建的全局强函数的时间衰减率如果在适当的附加条件下数据的频率较低，则可以获得解决方案。证明主要依赖于傅立叶分析对混合抛物线-双曲线系统的应用，以及改进的时间加权能量泛函。作为副产品，$$L^{q}$$L q – $$L^{r}$$ L r 类型的时间衰减率也在关键框架中捕获。