标题： 层流边界层在对流热传输中的作用 显示英文标题

标题： Laminar boundary layers in convective heat transport

摘要： 我们研究在高瑞利数和高普朗特数的条件下瑞利-贝纳德对流，即考虑一种流体被放置在一个容器中，在没有惯性效应的情况下，底部受到强烈的加热，顶部受到冷却。 尽管整体的动态由混沌的对流热流所表征，但水平容器板的边界层基本上是导热的，因此流体是静止的。 因此，平均温度在边界层中表现出线性分布。 在本文中，我们通过温度场的局部界限，严格研究了平均温度和边界层中的振荡。 此外，我们推导出温度分布确实接近水平容器板处的基本线性分布。 我们的结果在系统参数（例如瑞利数）上是均匀的，除了对数修正项。 我们分析中的一个重要工具是对流速度场的新类型哈迪估计，该估计可用于控制层中的流体运动。 温度场的界限是借助对流扩散方程的局部最大正则性估计得出的。 显示英文摘要

摘要： We study Rayleigh-Benard convection in the high-Rayleigh-number and high-Prandtl-number regime, i.e., we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia effects. While the dynamics in the bulk are characterized by a chaotic convective heat flow, the boundary layers at the horizontal container plates are essentially conducting and thus the fluid is motionless. Consequently, the average temperature exhibits a linear profile in the boundary layers. In this article, we rigorously investigate the average temperature and oscillations in the boundary layer via local bounds on the temperature field. Moreover, we deduce that the temperature profile is indeed essentially linear close to the horizontal container plates. Our results are uniform in the system parameters (e.g. the Rayleigh number) up to logarithmic correction terms. An important tool in our analysis is a new Hardy-type estimate for the convecting velocity field, which can be used to control the fluid motion in the layer. The bounds on the temperature field are derived with the help of local maximal regularity estimates for convection-diffusion equations.