Calculus of Variations and Geometric Measure Theory
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S. Chanillo - A. Malchiodi

Sharp bounds on the Nusselt number in Rayleigh-B\'enard convection

created by malchiodi on 06 Jan 2020
modified on 08 Jan 2020



Inserted: 6 jan 2020
Last Updated: 8 jan 2020

Year: 2020


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 mostly integral representations and cancellation properties, jointly with some Fourier analysis.


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