Abstract: In this talk, we will discuss the vanishing angular singularity limit of the Boltzmann equation. We first recall the derivation of Boltzmann's collision kernel for inverse power law interactions Us(r)=1/rs-1 for s>2 in dimension d=3. Then we study the limit of the non-cutoff kernel to the hard-sphere kernel. We also give precise asymptotic formulas of the singular layer near the angular singularity in the limit s→∞. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions weakly in L1 globally in time as s→∞ by looking at Arkeryd's construction of a weak solution to the Boltzmann equation for hard-sphere collisions and Villani's construction of an entropy solution for the Boltzmann equation for long-range inverse-power law potential. The spatially inhomogeneous case is still open.
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