We prove a new rigorous upper bound on the vertical heat transport for B\'enard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number $Ma \gg 1$ the Nusselt number $Nu$ is bounded asymptotically by $Nu \lesssim Ma^{2/7}(\ln Ma)^{-1/7}$. Key to our proof are a background temperature field with a hyperbolic profile near the fluid's surface, and new estimates for the coupling between temperature and vertical velocity.

中文翻译：

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无限普朗特数下 Bénard-Marangoni 对流垂直热传输的新边界

我们证明了具有无限普朗特数的二维或三维流体层的 B\'enard-Marangoni 对流的垂直热传输的新严格上限。准确地说，对于 Marangoni 数 $Ma \gg 1$，努塞尔特数 $Nu$ 渐近地由 $Nu \lesssim Ma^{2/7}(\ln Ma)^{-1/7}$ 界定。我们证明的关键是在流体表面附近具有双曲线轮廓的背景温度场，以及对温度和垂直速度之间耦合的新估计。