论文标题
无弹性玻尔兹曼方程的瞬间创建硬势而没有角度截止
Moments creation for the inelastic Boltzmann equation for hard potentials without angular cutoff
论文作者
论文摘要
本文关注的是无弹力的无弹性螺栓杆方程。我们在空间均匀的情况下工作。我们在碰撞内核上通用的硬势远程相互作用下建立了量度值解决方案的全球存在。此外，我们为制定测量值解决方案的多项式力矩提供了严格的证明，这是一种特殊特性，只能从艰难的潜在碰撞横截面中期望。这些证据至关重要地依赖于建立精致的povzner型不平等，而无弹性玻尔兹曼方程而没有角截止。我们需要的初始数据类别是一般的，因为我们只需要$（2+κ）$ - $κ> 0 $的限制性，并且不假定任何熵结合。
This paper is concerned with the inelastic Boltzmann equation without angular cutoff. We work in the spatially homogeneous case. We establish the global-in-time existence of measure-valued solutions under the generic hard potential long-range interaction on the collision kernel. In addition, we provide a rigorous proof for the creation of polynomial moments of the measure-valued solutions, which is a special property that can only be expected from hard potential collisional cross-sections. The proofs rely crucially on the establishment of a refined Povzner-type inequality for the inelastic Boltzmann equation without angular cutoff. The class of initial data that we require is general in the sense that we only require the boundedness of $(2+κ)$-moment for $κ>0$ and do not assume any entropy bound.
