Work

Local well-posedness for the periodic Boltzmann equation with constant collision kernel

Year: 2025

Type: article

Abstract: We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain T d , d ≥ 2 . Using tools developed in the study of nonlinear dispersive PDEs, we establish local well-posedness in L v 2 , r H x s for s > d 2 − 1 4 and r > d 2 , thereby addressing, in particular, a question posed by Gualdani–Mischler–Mouhot [25] . To reach the result, the main tool we establish is the L 4 Strichartz estimate for solutions to the corresponding linear equation.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.111288

Authors: E. Başakoğlu, C. Sun, N. Tzvetkov, Y. Wang

Institutions: ShanghaiTech University, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, Unité de Mathématiques Pures et Appliquées, Dalian University of Technology, University of Birmingham

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: UK Research and Innovation, Agence Nationale de la Recherche, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Dynamics of singular stochastic nonlinear dispersive PDEs, Probabilistic study of nonlinear Schrödinger equations on compact domains, Smooth Calculus for Low Regularity Random Data Partial Differential Equations

OpenAlex ID: W4404573610

FWCI:

Cites: 36

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Related to: 10