Temporal Regularity of Symmetric Stochastic p-Stokes Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-21 DOI:10.1007/s00021-024-00852-9

Jörn Wichmann

引用次数: 0

Abstract

We study the symmetric stochastic p-Stokes system, \(p \in (1,\infty )\), in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost \(-1/2\) temporal derivatives on a Besov scale. Second, we verify that the velocity u of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient \(V(\mathbb {\epsilon } u) = (\kappa + \left| \mathbb {\epsilon } u\right| )^{(p-2)/2} \mathbb {\epsilon } u\), \(\kappa \ge 0\), which measures the ellipticity of the p-Stokes system, has 1/2 temporal derivatives in a Nikolskii space.

查看原文本刊更多论文

对称随机 p-Stokes 系统的时间规律性

我们研究了有界域中的对称随机 p-Stokes 系统（p \in (1,\infty )\ ）。结果有两个方面：首先，我们证明了在解析弱解的情况下，与无发散随机力相关的随机压力在贝索夫尺度上具有几乎（-1/2）的时间导数。其次，我们验证了强解的速度 u 服从指数尼克尔斯基空间的 1/2 时间导数。此外，我们证明了非线性对称梯度（V(\mathbb {\epsilon } u) = (\kappa + \left| \mathbb {\epsilon } u\right| )^{(p-2)/2} \mathbb {\epsilon } u\)、\(\kappa \ge 0\) 测量 p-Stokes 系统的椭圆度，在 Nikolskii 空间有 1/2 的时间导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.