On Mittag-Leffler moments for the Boltzmann equation for hard potentials\n without cutoff

2015/12/21 by Maja Tasković, Ricardo J. Alonso, Tasković, Maja +5
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1512.06769

openalex publication_date 2015/12/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We establish the L¹ weighted propagation properties for solutions of the\nBoltzmann equation with hard potentials and non-integrable angular components\nin the collision kernel. Our method identifies null forms by angular averaging\nand deploys moment estimates of solutions to the Boltzmann equation whose\nsummability is achieved by introducing the new concept of Mittag-Leffler\nmoments - extensions of L¹ exponentially weighted norms. Such L¹ weighted\nnorms of solutions to the Boltzmann equation are, both, generated and\npropagated in time and the characterization of their corresponding\nMittag-Leffler weights depends on the angular singularity and potential rates\nin the collision kernel. These estimates are a fundamental step in order to\nobtain L^\∞ exponentially weighted estimates for solutions of the\nBoltzmann equation being developed in a follow up work.\n

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