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arXiv · 2609.02385

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

Zikai Chen·Chongyang Ren
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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.

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Zikai Chen, Chongyang Ren. 2026-09-02. Kinetic Fokker--Planck Equations with Drifts in a Supercritical Range. https://arxiv.org/abs/2609.02385

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