Global solutions in the critical Besov space for the non cutoff Boltzmann equation
Global solutions in the critical Besov space for the non cutoff Boltzmann equation
复制标题
DOI：
10.1016/j.jde.2016.06.017
复制
发表时间：
2015-12
期刊：
影响因子：
--
通讯作者：
Y. Morimoto;Shota Sakamoto
中科院分区：
文献类型：
--
作者：
Y. Morimoto;Shota Sakamoto
研究了无截止假设的玻尔兹曼方程。在扰动下，在临界Chemin-Lerner空间中建立了方程Cauchy问题的唯一整体解.为了分析方程的碰撞项，Chemin-Lerner范数与关于速度变量的非各向同性范数相结合，这产生能量估计的先验估计。结合交换子估计的局部存在性和Hahn-Banach扩张定理，得到了所需解。
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin–Lerner space. In order to analyze the collisional term of the equation, a Chemin–Lerner norm is combined with a non-isotropic norm with respect to a velocity variable, which yields an a priori estimate for an energy estimate. Together with local existence following from commutator estimates and the Hahn–Banach extension theorem, the desired solution is obtained.