Sagun Chanillo– Rutgers University
Date/Time/Location
Thursday, April 10th, 2025, 12:10 pm; Hill Center 705
Rayleigh-Benard Convection
The Rayleigh-Benard Equations are a model for the study of Convection in Fluids. Over the last 75 years, a lot of effort has gone into the study of the relation between various parameters that arise in this flow. About 70 years ago WVR Malkus conjectured a scaling relation between the Nusselt number and Rayleigh number in Rayleigh-Benard convection at infinite Prandtl number. This was further corroborated by the MIT colleague of Malkus, Louis Howard. Since then, physicists like Leo P. Kadanoff, S. Chandrasekhar the astrophysicist, have all given arguments in support of these scaling laws in addition to a large body of experiments in the lab and numerical simulations done by various engineers, aerodynamicists and physicists.
The first mathematically rigorous attempts to prove these scaling relations was by P. Constantin and C. Doering. This was followed by work by C. Doering , Felix Otto and M. Resznikoff and further works by Felix Otto and Christian Seis. They showed that the results conjectured 70 years ago by Malkus and Howard are indeed valid with logarithmic divergences.
We finally prove the conjecture of Malkus and Howard using tools from Harmonic Analysis, specifically Littlewood-Paley Theory and representation formulae. Our work is a joint work with Andrea Malchiodi(Scuola Normale Superiore, Pisa).