论文标题
具有整合角过渡的硬势的玻尔兹曼方程：强制性，指数尾巴速率和Lebesgue的集成性
The Boltzmann equation for hard potentials with integrable angular transition: Coerciveness, exponential tails rates, and Lebesgue integrability
论文作者
论文摘要
该手稿专注于一项广泛的调查，并通过将统一的凯奇问题方法的方法带入均匀的动力学方程，并通过将类似玻尔兹曼的碰撞运算符在粒子 - 粒子相互作用机制中的散射曲线的情况下，将凯奇问题的统一方法带到均匀的动力学方程。该作品着重于使用现代化研究解决方案属性的相关硬性案例。尽管可以找到许多讨论的结果在这些年来的文献上分布在几篇论文上，但我们带来了一个完整的程序，其中包括一种新的方法和唯一性定理，以确保适合良好的理论，对时刻的估计以及均匀的玻璃体流量的综合性传播。特别地，描述了经典多项式矩的详细计算作为强制性功能的上限，该计算表征了通过多项式的总结性获得的指数矩的速率。此外，在一般可集成的散射内核下进行了$ l^\ infty $规则性的均匀传播证明。一路上，仔细计算出出现的估计值的常数，从而改善了文献中的大多数先前退出结果。 For the non expert reader we also include a general discussion of the basic elements of the Boltzmann model and important key results for the understanding of the mathematical discussion of the equation and include an extensive set of references that enrich and motivate further discussions on Boltzmann flows for broader gas modeling configuration such as gas mixtures systems, polyatomic gases, multilinear collisional forms such as, ternary or quartic, to those derived from来自经典流体中光谱能波的对称制动量子平均场理论或弱湍流模型。
This manuscript focus on an extensive survey with new techniques on the problem of solving the Boltzmann flow by bringing a unified approach to the Cauchy problem to homogeneous kinetic equations with Boltzmann-like collision operators under integrability assumption of the scattering profile in the particle-particle interaction mechanism. The work focuses on the relevant hard potential case where the solution properties are studied with a modern take. While many of the discussed results can be found the literature spread over several papers along the years, we bring a complete program that includes a new approach to the existence and uniqueness theorem securing the well-posedness theory, to moments estimates, and integrability propagation for the homogeneous Boltzmann flow. In particular, a detailed calculation of classical polynomial moments upper bounds as function of the coerciveness is described, which characterized the rate of exponential moments obtained by summability of the polynomial ones. In addition, a proof of uniform propagation of $L^\infty$ regularity under general integrable scattering kernels is performed. Along the way, constants appearing in estimates are carefully calculated, improving most of previous exiting results in the literature. For the non expert reader we also include a general discussion of the basic elements of the Boltzmann model and important key results for the understanding of the mathematical discussion of the equation and include an extensive set of references that enrich and motivate further discussions on Boltzmann flows for broader gas modeling configuration such as gas mixtures systems, polyatomic gases, multilinear collisional forms such as, ternary or quartic, to those derived from symmetry braking quantum mean field theories or weak turbulence models from spectral energy waves in classical fluid.
