Low regularity Sobolev well-posedness for Vlasov--Poisson

Q: What type of study is this?

This is a Quantitative Study study.

In‐Jee Jeong; Sangwook Tae

doi:10.48550/arxiv.2510.02112

October 2, 2025Open Access

Low regularity Sobolev well-posedness for Vlasov--Poisson

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Key Points

Local well-posedness is achieved for the Vlasov–Poisson equation in high dimensions, enabling broader initial conditions.
Results demonstrate well-posedness in Sobolev spaces for initial distribution with compact support in velocity, enhancing understanding of solution behavior.
The findings imply that even data outside conventional L^p spaces can be managed within the Sobolev framework, expanding treatment possibilities.
This study fundamentally enhances the analysis of kinetic equations by addressing low regularity scenarios, aiding future research.

Implication

Analysis reveals local well-posedness in Sobolev spaces for Vlasov–Poisson equations, allowing specific initial conditions.

Abstract

We consider the Vlasov--Poisson equation on Rⁿ × Rⁿ with n ≥ 3. We prove local well-posedness in Hˢ(Rⁿ × Rⁿ) with $s> n/2-1/4$, for initial distribution f₀ ∈ Hˢ(Rⁿ × Rⁿ) having compact support in v. In particular, data not belonging to Lᵖ(Rⁿ × Rⁿ) for large p are allowed.

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Cite This Study

Jeong et al. (2025) studied this question.

synapsesocial.com/papers/68e25559d6d66a53c247500a https://doi.org/10.48550/arxiv.2510.02112

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Low regularity Sobolev well-posedness for Vlasov--Poisson

Key Points

Implication

Abstract

Discussion

Cite This Study

Low regularity Sobolev well-posedness for Vlasov--Poisson

Key Points

Implication

Abstract

Discussion

Cite This Study

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