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

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.

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Cited by in corpus (2)

• Stability of vacuum for the Landau equation with hard potentials
• Global solution of the $3D$ relativistic Vlasov-Maxwell system for the large radial data