论文标题
雷利 - 贝纳德对流中的努塞尔特数字的尖锐界限和通过Carleson措施的双线性估算值
Sharp bounds on the Nusselt number in Rayleigh-Bénard convection and a bilinear estimate via Carleson measures
论文作者
论文摘要
我们证明了流体动力学的猜想，这些动力学涉及无限prandtl数量限制中热传输的最佳界限。由于君士坦丁丁丁和奥托 - 赛的最大原理特性，这相当于在大宽度带中的四阶方程的水平周期溶液中证明了A-Priori边界。此处使用傅立叶分析，积分表示和由于Coifman和Meyer引起的双线性估算获得了此类界限，该估计使用了Fefferman对BMO函数的Carleson测量表征。
We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit. Due to a maximum principle property for the temperature exploited by Constantin-Doering and Otto-Seis, this amounts to proving a-priori bounds for horizontally-periodic solutions of a fourth-order equation in a strip of large width. Such bounds are obtained here using Fourier analysis, integral representations, and a bilinear estimate due to Coifman and Meyer which uses the Carleson measure characterization of BMO functions by Fefferman.
