论文标题
在对具有软电势的无弹性玻尔兹曼方程的尺寸有价值的解决方案上
On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials
论文作者
论文摘要
本文的目的是将Morimoto-Wang-Yang给出的弹性相互作用中的测量值解决方案的存在结果扩展到弹性相互作用中的玻尔兹曼方程，并将其具有中等软势的无弹性玻尔兹曼方程，也是我们在非弹性Maxwellian Molecules案例中的广泛结果。我们通过微妙的紧凑性论证证明了在Grad的角度截止假设和无限能量初始基准的非切割解决方案下的测量值解决方案以及非切割解决方案的存在的存在和唯一性。另外，对于获得的测量值解决方案，矩传的繁殖和能量耗散特性也是合理的。
The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto-Wang-Yang, to the inelastic Boltzmann equation with moderately soft potentials, also as an extensive work of our preceding result in the inelastic Maxwellian molecules case. We prove the existence and uniqueness of measure-valued solution under Grad's angular cutoff assumption, as well as the existence of non-cutoff solution, for both finite and infinite energy initial datum, by a delicate compactness argument. In addition, the moments propagation and energy dissipation properties are justified for the obtained measure-valued solution as well.
