SHUBIN REGULARITY FOR THE RADIALLY SYMMETRIC SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH DEBYE-YUK

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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.
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