Shubin regularity for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential

TL;DR

This paper demonstrates that solutions to the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential exhibit smoothing effects similar to fractional logarithmic harmonic oscillators, belonging to Shubin spaces.

Contribution

It establishes the regularity of solutions in Shubin spaces for the Boltzmann equation with Debye-Yukawa potential, revealing a new smoothing property.

Findings

Solutions belong to Shubin spaces.

Smoothing effect analogous to fractional logarithmic harmonic oscillator.

Regularity results for the 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.