线性索波列夫传输中的极端时间间歇性:几乎平滑的非唯一解

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Alexey Cheskidov, Xiaoyutao Luo
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引用次数: 0

摘要

我们重温时间间歇性概念,以获得线性输运方程的尖锐非唯一性结果。我们为空间维数 d≥ 2 中的所有 p<∞ 构建了具有尖锐 Sobolev 正则性的无发散向量场 Lt1W1,p,其输运方程在所有 p<∞ 和 k∈ℕ 条件下都接受属于 LtpCk 的非唯一弱解。特别是,我们的结果表明,DiPerna-Lions 理论唯一性中的时间可控性假设是至关重要的。同样的结果也适用于任意维数 d≥ 2 的具有任意大阶扩散算子的输运扩散方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Extreme temporal intermittency in the linear Sobolev transport: Almost smooth nonunique solutions

We revisit the notion of temporal intermittency to obtain sharp nonuniqueness results for linear transport equations. We construct divergence-free vector fields with sharp Sobolev regularity Lt1W1,p for all p < in space dimensions d 2 whose transport equations admit nonunique weak solutions belonging to LtpCk for all p < and k . In particular, our result shows that the time-integrability assumption in the uniqueness of the DiPerna–Lions theory is essential. The same result also holds for transport-diffusion equations with diffusion operators of arbitrarily large order in any dimensions d 2.

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来源期刊
Accounts of Chemical Research
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.
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