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Sharp bounds on the Nusselt number in Rayleigh-B\'enard convection and a bilinear estimate via Carleson measures - MaRDI portal

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Sharp bounds on the Nusselt number in Rayleigh-B\'enard convection and a bilinear estimate via Carleson measures

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Publication:6503905

arXiv2001.01662MaRDI QIDQ6503905

Author name not available (Why is that?)


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.












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