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arXiv · 2610.17319

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

Jean-François Jabir·Damir Kinzebulatov·Chengjun Yue
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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.

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Jean-François Jabir, Damir Kinzebulatov, Chengjun Yue. 2026-10-12. Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups. https://arxiv.org/abs/2610.17319

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