Work

Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range

Year: 2026

Type: preprint

Abstract: We investigate kinetic Fokker--Planck equations with rough divergence-free drifts in anisotropic mixed Lebesgue spaces. The divergence-free structure yields an energy cancellation that remains effective under kinetic localization. Combining this cancellation with anisotropic regularization estimates and a De Giorgi iteration, we establish local boundedness for weak subsolutions and, consequently, global well-posedness for the Cauchy problem in a scaling-supercritical regime.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02385

Authors: Chen, Zikai, Ren, Chongyang

Institutions: University of Science and Technology of China, Wuhan University, Kyoto University

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: China Postdoctoral Science Foundation, China Scholarship Council

OpenAlex ID: W7207705034

Cites: 19

Cited by: 1

Related to: 10