Global existence of solutions of the Nordstr\"om-Vlasov system in two space dimensions
Hayoung Lee
TL;DR
This paper proves the global existence of smooth solutions for the Nordstr"om-Vlasov system in two space dimensions, modeling collisionless particles under a scalar gravitational theory, with integral representations of derivatives aiding the proof.
Contribution
It establishes the first global existence result for smooth solutions of the 2D Nordstr"om-Vlasov system using integral representations of derivatives.
Findings
Global existence of smooth solutions for large data
Integral representations of derivatives of the field
Modeling collisionless particles in scalar gravity
Abstract
The dynamics of a self-gravitating ensemble of collisionless particles is modeled by the Nordstr\"om-Vlasov system in the framework of the Nordstr\"om scalar theory of gravitation. For this system in two space dimensions, integral representations of the first order derivatives of the field are derived. Using these representations we show global existence of smooth solutions for large data.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Cosmology and Gravitation Theories · Quantum Electrodynamics and Casimir Effect