Local well-posedness of the Vlasov-Poisson-Landau system and related models

Patrick Flynn

doi:10.3934/krm.2024027

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2025, Volume 18, Issue 4: 583-608. Doi: 10.3934/krm.2024027

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Local well-posedness of the Vlasov-Poisson-Landau system and related models

Patrick Flynn

University of California, Los Angeles, United States of America

Received: March 2024

Revised: November 2024

Early access: December 2024

Published: August 2025

Patrick Flynn was partially supported by the National Science Foundation Graduate Research Fellowship, Grant No. 2040433. Thank you to Yan Guo, Benoît Pausader and Timur Yastrzhembskiy for helpful conversations and suggestions.

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Abstract

We prove local well-posedness for the Vlasov-Poisson-Landau system and the variant with massless electrons in a 3D periodic spatial domain for large initial data. This is accomplished by propagating weighted anisotropic $ L^2 $-based Sobolev norms. In the case of the massless electron system, we also carry out an analysis of the Poincaré-Poisson system. This is a companion paper to the author's previous work with Yan Guo [6].

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Mathematics Subject Classification: Primary: 35Q83, 82C40.

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References

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