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The Harnack inequality fails for nonlocal kinetic equations (2405.05223v2)

Published 8 May 2024 in math.AP and math.PR

Abstract: We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest equation in this theory, the fractional Kolmogorov equation. Our result reflects a purely nonlocal phenomenon since the Harnack inequality holds true for local kinetic equations like the Kolmogorov equation.

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