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Nonlinearity, Complexity and Foundations in Mathematics

Sharp bounds on the Nusselt number in Rayleigh-Bénard convection

speaker: Andrea Malchiodi (Scuola Normale Superiore)

abstract: We analyze the problem in fluid dynamics of deriving bounds for heat transportation in the infinite Prandtl number limit. Due to a maximum principle property for the temperature, this amounts to proving a-priori bounds for horizontally-periodic solutions of a fourth-order equation in a strip of large width with both Dirichlet and Neumann data. We obtain such bounds 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. This is joint work with S.Chanillo.

timetable:
Wed 11 Sep, 14:30 - 15:05, Aula Dini
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