What question did this study set out to answer?

This work aims to prove the global existence and uniqueness of mild solutions to the relativistic Vlasov-Maxwell-Fokker-Planck system.

June 27, 2026AxiomsOpen Access

Global Existence of Solutions to the Cauchy Problem for the Relativistic Vlasov–Maxwell–Fokker–Planck System in Low-Regularity Spaces

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Authors

YFYingzhe FanNanyang Normal University DHDali HuNanyang Normal University

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Implication

Randomized trial establishes global solutions to the relativistic VMFP system in low-regularity spaces, highlighting applicability for complex kinetic equations.

Key Points

This work aims to prove the global existence and uniqueness of mild solutions to the relativistic Vlasov-Maxwell-Fokker-Planck system.
Utilized a mixed-norm space Lk1LT∞Lp2 for kinetic equations which requires low regularity.
Employed macro-micro decomposition to estimate macroscopic and microscopic behaviors.
Derived a uniform a priori bound on energy functional under small initial perturbation.
Established global existence of mild solutions near Maxwellian equilibrium.
Demonstrated uniqueness of solutions despite low regularity constraints.
Provided estimates indicating validity of the proposed low-regularity framework.

Cite This Study

Fan et al. (2026) studied this question.

synapsesocial.com/papers/6a3f6871aea7db3c1953f7f8 https://doi.org/10.3390/axioms15070471

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Implication

Randomized trial establishes global solutions to the relativistic VMFP system in low-regularity spaces, highlighting applicability for complex kinetic equations.

Global Existence of Solutions to the Cauchy Problem for the Relativistic Vlasov–Maxwell–Fokker–Planck System in Low-Regularity Spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

Global Existence of Solutions to the Cauchy Problem for the Relativistic Vlasov–Maxwell–Fokker–Planck System in Low-Regularity Spaces

Discussion

Member takes

Implication

Key Points

Cite This Study

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