• Corpus ID: 252568130

Vanishing angular singularity limit to the hard-sphere Boltzmann equation

@inproceedings{Jang2022VanishingAS,
  title={Vanishing angular singularity limit to the hard-sphere Boltzmann equation},
  author={Jin Woo Jang and Bernhard Kepka and Alessia Nota and Juan J. L. Vel'azquez},
  year={2022}
}

• Jin Woo Jang, Bernhard Kepka, +1 author Juan J. L. Vel'azquez
• Published 28 September 2022
• Mathematics

. 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 pre- cise asymptotic formulas of the singular layer near θ (cid:39) 0 in the limit s → ∞ . Consequently, we show that solutions to the homogeneous Boltzmann equation converge to the respective solutions.