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Watch a 51-minute lecture from the Institute for Advanced Study's Analysis and Mathematical Physics series where Professor Robert Strain from the University of Pennsylvania explores the Boltzmann equation in the diffusive limit within a channel domain, focusing on 3D kinetic Couette flow. Learn about the first-order approximation of solutions governed by the perturbed incompressible Navier-Stokes-Fourier system and discover how 3D kinetic Couette flow converges to 1D steady planar kinetic Couette flow in the absence of external forces. Gain insights into advanced mathematical techniques including Fourier transforms, anisotropic Chemin-Lerner function spaces using Wiener algebra, and the Caflisch decomposition combined with L2∩L∞ technique for managing large velocity growth. Begin with a comprehensive introduction suitable for non-experts before diving into the collaborative research conducted with Renjun Duan, Shuangqian Liu, and Anita Yang.
