论文标题
消失的角度奇异性极限限制了硬球方程
Vanishing angular singularity limit to the hard-sphere Boltzmann equation
论文作者
论文摘要
在本说明中，我们研究了Boltzmann的碰撞内核，用于逆权法律互动$ u_s（r）= 1/r^{s-1} $ for $ s> 2 $ in Dimension $ d = 3 $。我们证明了非切割内核对硬球核的极限，并在限制$ s \ to \ infty $的$θ\ simeq 0 $附近给出了奇异层的精确渐近公式。因此，我们表明，均质玻尔兹曼方程的解决方案会融合到相应的解决方案。
In this note we study Boltzmann's collision kernel for inverse power law interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $ d=3 $. We prove the limit of the non-cutoff kernel to the hard-sphere kernel and give precise asymptotic formulas of the singular layer near $θ\simeq 0$ in the limit $ s\to \infty $. Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions.
