Inserted: 6 jan 2020
Last Updated: 8 jan 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.