Shubin Regularity for the Radially Symmetric Spatially Homogeneous Boltzmann Equation with Debye-Yukawa Potential

Abstract

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.

Cauchy problem to the homogeneous Boltzmann equation with Debye–Yukawa potential for measure initial datum

“…In the present work, setting the angular function b satisfies the Debye-Yukawa potential (1.2) for s > 0, based upon [11] and our recent results of [6], [7] for the Cauchy problem to the linearized homogeneous Boltzmann equation with Debye-Yukawa potential, we intend to prove the result in [12] for the probability measure initial datum. Now we introduce the probability measure.…”