Propagation of regularity and long time behavior of 3D massive relativistic transport equation I: Vlasov-Nordström system

2018/04/18 by Xuecheng Wang, Wang, Xuecheng · 5 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Field (mathematics) #Fourier transform #Gas Dynamics and Kinetic Theory #Mathematical physics #Mathematics #Physics #Plasma #Pure mathematics #Quantum electrodynamics #Quantum mechanics #Scattering #Vlasov equation #Wave equation #math.AP

paper · pdf · doi:10.48550/arxiv.1804.06560

published in arXiv (Cornell University) (Cornell University) · Reorganized to improve presentation

openalex publication_date 2018/04/18 · openalex created_date 2018/04/24 · arxiv created 2020/02/18 · arxiv updated 2020/02/19 · openalex updated_date 2026/08/05

Abstract

In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable for general Vlasov-Wave type coupled systems. By combining the strength of Klainerman vector field method and Fourier method, we prove global regularity and scattering for the 3D massive relativistic Vlasov-Nordström system for small initial data without any compact support assumption, which is widely used in the literature for the study of Vlasov solution.

Citations

• Absence of shocks in an initially dilute collisionless plasma
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data

Cited by

• Global existence of the irrotational Euler-Nordström equations with a positive cosmological constant: The gravitational field equation

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• Propagation of regularity and long time behavior of the 3D massive relativistic transport equation II: Vlasov-Maxwell system
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• Global solution of the 3D relativistic Vlasov-Maxwell system for the large radial data
• Asymptotic properties of small data solutions of the Vlasov-Maxwell system in high dimensions