论文标题
关于cauchy问题的截止玻尔兹曼方程，并带有少量初始数据
On the Cauchy problem for the cutoff Boltzmann equation with small initial data
论文作者
论文摘要
我们证明，对于软势模型$ -1 \ 1 \ leqγ<0 $，在三维空间中的小初始数据中，cauchy boltzmann方程的cauchy问题的全球存在。因此，我们的结果在作者先前的工作中，在三维空间中，在三维空间中弥补了$γ= -1 $的差距，在这种工作中，不正确地使用了损失项的估计值。 Chen，Denlinger和Pavlović最近确定了二维空间中$γ= 0 $的另一个差距。初始数据$ f_ {0} $是非负的，在加权$ l^{3} _ {x，v} $中小，加权$ l^{15/8} _ {x，v} $有限。我们还表明，该溶液相对于动力学运输算子散射。这项工作的新颖贡献在于根据加权估计值探索增益项的对称特性。在应用Strichartz估计值时，它是解决模型$ -1 <γ<0 $的关键成分。
We prove the global existence of the non-negative unique mild solution for the Cauchy problem of the cutoff Boltzmann equation for soft potential model $-1\leq γ< 0$ with the small initial data in three dimensional space. Thus our result fixes the gap for the case $γ=-1$ in three dimensional space in the authors' previous work where the estimate for the loss term was improperly used. The other gap there for the case $γ=0$ in two dimensional space is recently fixed by Chen, Denlinger and Pavlović. The initial data $f_{0}$ is non-negative, small in weighted $L^{3}_{x,v}$ and finite in weighted $L^{15/8}_{x,v}$. We also show that the solution scatters with respect to the kinetic transport operator. The novel contribution of this work lies in the exploration of the symmetric property of the gain term in terms of weighted estimate. It is the key ingredient for solving the model $-1<γ<0$ when applying the Strichartz estimates.
