Smoothing effect and Cauchy problem for radially symmetric homogeneous Boltzmann equation with Debye-Yukawa potential of Shubin class initial datum
Smoothing effect and Cauchy problem for radially symmetric homogeneous Boltzmann equation with Debye-Yukawa potential of Shubin class initial datum
复制标题
Shubin类初始数据具有德拜-汤川势的径向对称齐次Boltzmann方程的平滑效应与柯西问题
DOI：
10.1016/j.jmaa.2017.10.053
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发表时间：
2018
影响因子：
1.3
通讯作者：
Shang Yueyun
中科院分区：
文献类型：
--
作者：
Li Hao Guang;Shang Yueyun
本文研究了带Debye-Yukawa势的径向对称齐次非截断Boltzmann方程的Cauchy问题，初值为具有负指数的Shubin型空间，可用谐振子的谱分解来刻画，且为Maxwell分布的小扰动.负指数的Shubin型空间包含概率测度。基于谱分解，构造了具有Shubin型初值的弱解，并证明了光滑效应对该Cauchy问题解的影响。
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.