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Abstract In this paper, we study the Cauchy problem for the radially symmetric homogeneous non-cutoff Boltzmann equation with Debye–Yukawa potential, the initial datum belongs to Shubin type space of the… Click to show full abstract
Abstract In this paper, we study the Cauchy problem for the radially symmetric homogeneous non-cutoff Boltzmann equation with Debye–Yukawa potential, the initial datum belongs to Shubin type space of the negative index which can be characterized by spectral decomposition of the harmonic oscillator, and it is a small perturbation of Maxwellian distribution. The Shubin type space of negative index contains the probability measures. Based on the spectral decomposition, we construct the weak solution with Shubin type class initial datum and prove the smoothing effect for the solution to this Cauchy problem.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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