Shubin regularity for the radially symmetric spatially homogeneous   Boltzmann equation with Debye-Yukawa potential
  In this work, we study the Cauchy problem for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential. We prove that this Cauchy problem enjoys the same smoothing effect as the Cauchy problem defined by the evolution equation associated to a fractional logarithmic harmonic oscillator. To be specific, we can prove the solution of the Cauchy problem belongs to Shubin spaces. 
L\'eo Glangetas, Hao-Guang Li
math.AP