2012/05/08 by Renjun Duan, Duan, Renjun · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.1205.1635
openalex publication_date 2012/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range collision kernel of soft potentials, particularly including the classical Coulomb collision, provided that initial data is smooth enough and decays in velocity variable fast enough. As a byproduct, the convergence rates of solutions are also obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of this complex system such as dispersion of the macro component in ℝ3, singularity of the long-range collisions and regularity-loss of the electromagnetic field.