Work

The Harnack inequality fails for nonlocal kinetic equations

Year: 2024

Type: article

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.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.110030

Authors: Moritz Kassmann, Marvin Weidner

Institutions: Bielefeld University, Universitat de Barcelona

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510

Funders: Deutsche Forschungsgemeinschaft, European Research Council, Agencia Estatal de Investigación, H2020 European Research Council