Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

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

[BibTeX]

Preprint

Inserted: 6 jan 2020
Last Updated: 8 jan 2020

Year: 2020

Abstract:

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.


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1