Global existence of weak solutions to the nonlinear Vlasov-Fokker-Planck equation

2023/11/14 by Young-Pil Choi, Choi, Young-Pil, Byung-Hoon Hwang +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2311.07922

openalex publication_date 2023/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the nonlinear Vlasov-Fokker-Planck equation with fixed collision frequency. We establish the global-in-time existence of weak solutions to the equation with large initial data. Moreover, we show that our solution satisfies the conservation laws of mass, momentum, and energy, and Boltzmann's H-theorem.

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