$${mathbb {R}}^3$ 中可压缩纳维-斯托克斯-科特韦格系统的时空衰减率

IF 0.7 4区数学 Q2 MATHEMATICS Bulletin of The Iranian Mathematical Society Pub Date : 2024-09-13 DOI:10.1007/s41980-024-00916-6

Wanping Wu, Yinghui Zhang

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引用次数: 0

摘要

我们研究了可压缩 Navier-Stokes-Korteweg 系统三维 Cauchy 问题解的时空衰减率。基于之前该系统的时空衰减结果，对于任意整数（N\ge 3\），k\left( \in \left[ 0、右）解在加权空间 $H^{N-k}_{\gamma }$ 的阶空间导数是（t^{-\frac{3}{4}-\frac{k}{2}+\gamma }\ ）。我们的方法主要涉及精细的加权能量估计和插值技巧。

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Space-time Decay Rate for the Compressible Navier–Stokes–Korteweg System in $${\mathbb {R}}^3$$

We investigate the space-time decay rate of solution to the 3D Cauchy problem of the compressible Navier–Stokes–Korteweg system. Based on the previous temporal decay results for this system, it is shown that for any integer $N\ge 3$, the space-time decay rate of $k\left( \in \left[ 0, N\right] \right) $-order spatial derivative of the solution in weighted space $H^{N-k}_{\gamma }$ is $t^{-\frac{3}{4}-\frac{k}{2}+\gamma }$. Our methods mainly involve delicate weighted energy estimates and interpolation trick.

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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

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期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.

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