• Corpus ID: 252568130

Vanishing angular singularity limit to the hard-sphere Boltzmann equation

  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},
. 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. 

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