The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand–Shilov smoothing effect - Archive ouverte HAL
Article Dans Une Revue Journal of Differential Equations Année : 2017

The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand–Shilov smoothing effect

Résumé

In this paper, we study the Cauchy problem for the radially symmetric homogeneous non-cutoff Boltzmann equation with Maxwellian molecules, the initial datum belongs to Shubin 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 space of the negative index contains the probability measures. Based on this spectral decomposition, we construct the weak solution with Shubin class initial datum, we also prove that the Cauchy problem enjoys Gelfand–Shilov smoothing effect, meaning that the smoothing properties are the same as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator.

Dates et versions

hal-02343762 , version 1 (03-11-2019)

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Citer

Hao-Guang Li, Chao-Jiang Xu. The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand–Shilov smoothing effect. Journal of Differential Equations, 2017, 263 (8), pp.5120-5150. ⟨10.1016/j.jde.2017.06.010⟩. ⟨hal-02343762⟩
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