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Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups

Year: 2026

Type: preprint

Abstract: We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form $L^\infty+M^q_K$ force field which can produce local blow-ups due to strong attraction to a submanifold. Our approach is based on the fractional representation for the Duhamel series of the equation and on establishing kinetic Adams-type estimates. Accordingly, we construct weak solutions of Brownian-driven kinetic SDEs in a critical Morrey set-up, obtain kinetic Krylov-type estimates and a strongly continuous Feller propagator, and establish uniqueness criteria for a large class of weak solutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.17319

Authors: Jabir, Jean-François, Kinzebulatov, Damir, Yue, Chengjun

Institutions: Université Laval, National Research University Higher School of Economics

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221806499

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