2022/03/02 by Xuecheng Wang, Wang, Xuecheng
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Gas Dynamics and Kinetic Theory #Pulsars and Gravitational Waves Research #math.AP
paper · pdf · doi:10.48550/arxiv.2203.01199
openalex publication_date 2022/03/02 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This is the first part of a two-paper sequence establishing the global existence of 3D relativistic Vlasov-Maxwell system (RVM) for arbitrarily large smooth localized initial data with cylindrical symmetry. This paper employs Part II's pointwise estimates, developed independently of Part I, as fundamental tools to demonstrate the iterative smoothing scheme (ISS), which is originated and inspired by the work of Klainerman-Staffilani(2002). Using ISS and a novel singular weighted space-time estimate for the distribution function, we prove upper bounds for the projection and full velocity characteristics via a standard bootstrap argument. Using the classic momentum method, we find that the high order momentum at most grows polynomially in time. This further implies that the L^∞x-norm of the electromagnetic field, ‖(E(t),B(t)‖L^∞x, also grows at most polynomially over time. Consequently, this verifies the continuation criteria obtained by Luk-Strain (2014). As a result, the energy function of 3D RVM system doesn't blow up in finite time, thereby establishing global existence.