论文标题
$ l^p $估计的繁殖空间相对论鲍尔茨曼方程
Propagation of $L^p$ estimates for the Spatially Homogeneous Relativistic Boltzmann Equation
论文作者
论文摘要
在本文中，我们证明了$ l^p $上限的传播，用于空间均匀的相对论鲍尔茨曼方程，以$ 1 <p <\ p <\ infty $。我们考虑了相对论\ textit {hard ball}的情况。我们的证明是基于对收益操作员的相对动量，规律性和$ l^p $估算之间相互关系的详细研究，相对论性carleman代表的发展以及相对论高空的$ e^{v _*} _ {v'-v'-v} $的几个估计值。我们还为\ textit {相对momenta} $ g（v，v _*），$ $ g（v，v，v'）$和$ g（v'，v'，v _*）$得出了一个毕达哥拉斯定理，在减少动量奇异性方面具有至关重要的作用。
In this paper, we prove the propagation of $L^p$ upper bounds for the spatially homogeneous relativistic Boltzmann equation for any $1<p<\infty$. We consider the case of relativistic \textit{hard ball} with Grad's angular cutoff. Our proof is based on a detailed study of the interrelationship between the relative momenta, the regularity and the $L^p$ estimates for the gain operator, the development of the relativistic Carleman representation, and several estimates on the relativistic hypersurface $E^{v_*}_{v'-v}$. We also derive a Pythagorean theorem for the \textit{relative momenta} $g(v,v_*),$ $g(v,v')$, and $g(v',v_*)$, which has a crucial role in the reduction of the momentum singularity.
