Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data

2008/04/10 by Ricardo J. Alonso, Alonso, Ricardo J.
Engineering · Mathematics · #76P05 #82C40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Particle Dynamics in Fluid Flows

paper · pdf · doi:10.48550/arxiv.0804.1606

openalex publication_date 2008/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The technique used to derive the result is the well known iteration process of Kaniel and Shinbrot.

Related

• Global existence for the Boltzmann equation in L^r_v L^∞_t L^∞_x spaces
• Local solutions for the Boltzmann equation
• Bounded Solutions of the Boltzmann Equation in the Whole Space
• Solution to the Boltzmann equation in velocity-weighted Chemin-Lerner type spaces
• Global mild solution with polynomial tail for the Boltzmann equation in the whole space