On geometric and analytic mixing scales: comparability and convergence rates for transport problems
On geometric and analytic mixing scales: comparability and convergence rates for transport problems
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在几何和解析混合尺度上：传输问题的可比性和收敛率
DOI：
10.2140/paa.2019.1.543
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C. Zillinger
中科院分区：
文献类型：
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作者：
C. Zillinger
在这篇文章中，我们感兴趣的被动标量问题的解决方案的几何和分析混合规模。在这里，我们表明，这两个概念是可比的后，可能删除大规模的投影。为了讨论我们的技术在一个透明的方式，我们进一步介绍了一个二元模型问题。
在我们的文章的第二部分中，我们考虑的问题的急剧衰减率为两个规模的索博列夫经常的初始数据时，根据运输方程和相关的主动和被动标量方程的发展。在这里，我们表明，略快于预期的代数衰减率是最佳的。
In this article we are interested in the geometric and analytic mixing scales of solutions to passive scalar problems. Here, we show that both notions are comparable after possibly removing large scale projections. In order to discuss our techniques in a transparent way, we further introduce a dyadic model problem.
In a second part of our article we consider the question of sharp decay rates for both scales for Sobolev regular initial data when evolving under the transport equation and related active and passive scalar equations. Here, we show that slightly faster rates than the expected algebraic decay rates are optimal.