论文标题
de Giorgi的非切割玻尔兹曼方程的论点，具有软电位
De Giorgi Argument for non-cutoff Boltzmann equation with soft potentials
论文作者
论文摘要
在本文中，我们考虑了在$ l^\ infty $设置中具有软潜力的非切割Boltzmann方程的全球范围。我们表明，当初始数据接近平衡，并且扰动在$ l^2 \ cap l^\ infty $ polyenmial加权空间中时，Boltzmann方程在加权$ L^2 \ 2 \ cap l^\ infty $空间中具有全球解决方案。证明的成分在于强烈的平均引理，非切割玻尔兹曼方程的新多项式加权估计以及\ cite {amsy2}中开发的$ l^2 $级别集合di giorgi迭代方法。还证明了$ l^2 $和$ l^\ infty $空间的融合。
In this paper, we consider the global well-posedness to the non-cutoff Boltzmann equation with soft potential in the $L^\infty$ setting. We show that when the initial data is close to equilibrium and the perturbation is small in $L^2 \cap L^\infty$ polynomial weighted space, the Boltzmann equation has a global solution in the weighted $L^2 \cap L^\infty$ space. The ingredients of the proof lie in strong averaging lemma, new polynomial weighted estimate for the non-cutoff Boltzmann equation and the $L^2$ level set Di Giorgi iteration method developed in \cite{AMSY2}. The convergence to the equilibrium state in both $L^2$ and $L^\infty$ spaces is also proved.
