Moment classification of infinite energy solutions to the homogeneous Boltzmann equation
Yoshinori Morimoto, Shuaikun Wang, Tong Yang
TL;DR
This paper classifies characteristic functions in Fourier space based on moment constraints and constructs measure-valued solutions to the homogeneous Boltzmann equation with specified initial moments.
Contribution
It introduces a detailed classification of characteristic functions by moments and constructs solutions with exact initial moment conditions.
Findings
Classification of characteristic functions by moments
Construction of measure-valued solutions with prescribed moments
Exact moment condition adherence in solutions
Abstract
In this paper, we will introduce a precise classification of characteristic functions in the Fourier space according to the moment constraint in the physical space of any order. Based on this, we construct measure valued solutions to the homogeneous Boltzmann equation with the exact moment condition as the initial data.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Numerical methods in inverse problems · Advanced Mathematical Physics Problems