| 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 $U_s(r)=1/r^{s-1}$ 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 $s\to \infty$. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions weakly in $L^1$ globally in time as $s\to \infty$ 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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