系数在一个方向上可测的平稳Stokes系统的lq估计

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-04-01 DOI:10.1142/s1664360719500048

Hongjie Dong, Doyoon Kim

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引用次数: 15

摘要

研究了全空间、半空间和有界Lipschitz域上的变系数平稳Stokes系统。在整个和半空间中，我们得到了一个先验的[公式:见文]-当系数仅仅是一个固定方向上的可测量函数时的任何[公式:见文]的估计。对于具有小Lipschitz常数的有界Lipschitz域上的系统，我们得到了一个[公式:见文]-当系数仅仅是一个方向上的可测量函数并且在每个小球的正交方向上具有局部小的平均振荡时，我们估计并证明了任何[公式:见文]的可解性，其中方向允许依赖于球。

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Lq-Estimates for stationary Stokes system with coefficients measurable in one direction

We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori [Formula: see text]-estimates for any [Formula: see text] when the coefficients are merely measurable functions in one fixed direction. For the system on bounded Lipschitz domains with a small Lipschitz constant, we obtain a [Formula: see text]-estimate and prove the solvability for any [Formula: see text] when the coefficients are merely measurable functions in one direction and have locally small mean oscillations in the orthogonal directions in each small ball, where the direction is allowed to depend on the ball.

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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.