浮力对趋化奇异性的抑制

IF 2.4 1区 数学 Q1 MATHEMATICS
Zhongtian Hu, Alexander Kiselev, Yao Yao
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引用次数: 0

摘要

在patak - keller - segel方程下的趋化奇点形成是一个被广泛研究的现象。近年来,研究表明,如果流体流动具有混合或扩散增强特性,且其振幅足够强,那么流体平流的存在可以阻止奇点的形成——据推测,这种效应适用于更一般类型的非线性偏微分方程。在本文中,我们考虑在不可压缩多孔介质中,patak - keller - segel方程与服从达西定律的流体流动通过浮力耦合。我们证明了与被动平流相比,这种主动流体耦合能够在任意小的耦合强度下抑制奇点的形成,即系统总是具有全局正则解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Suppression of Chemotactic Singularity by Buoyancy

Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest the singularity formation given that the fluid flow possesses mixing or diffusion enhancing properties and its amplitude is sufficiently strong - this effect is conjectured to hold for more general classes of nonlinear PDEs. In this paper, we consider the Patlak-Keller-Segel equation coupled with a fluid flow that obeys Darcy’s law for incompressible porous media via buoyancy force. We prove that in contrast with passive advection, this active fluid coupling is capable of suppressing singularity formation at arbitrary small coupling strength: namely, the system always has globally regular solutions.

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来源期刊
CiteScore
3.70
自引率
4.50%
发文量
34
审稿时长
6-12 weeks
期刊介绍: Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis. GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016. Publishes major results on topics in geometry and analysis. Features papers which make connections between relevant fields and their applications to other areas.
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