Nonlinear Asymptotic Stability of 3D Relativistic Vlasov-Poisson systems

Abstract

Motivated by the stellar wind ejected from the upper atmosphere (Corona) of a star, we explore a boundary problem of the two-species nonlinear relativistic Vlasov-Poisson systems in the 3D half space in the presence of a constant vertical magnetic field and strong background gravity. We allow species to have different mass and charge (as proton and electron, for example). As the main result, we construct stationary solutions and establish their nonlinear dynamical asymptotic stability in time and space.

Bio

I joined the Department of Mathematics as an assistant professor in August 2024. I received my B.S. in Mathematics from Shanghai Jiao Tong University in 2014, my M.S. in Mathematics from the University of Wisconsin-Madison in 2015, and my Ph.D. in Mathematics from the University of Wisconsin-Madison in 2021. Prior to joining UL Lafayette, I served as a Zassenhaus Assistant Professor in the Department of Mathematics at The Ohio State University. My research focuses on applying dynamical systems to mathematical biology or biochemistry and applied partial differential equations in mathematical physics, with three distinct areas of emphasis: (i) investigation of the dynamical equivalence between reaction models and the relationship between reaction rates and graph structures with complex-balanced realizations, (ii) analysis of the network structure in input-output networks to characterize homeostasis points in the input-output function, (iii) exploration of the existence and regularity of solutions for the kinetic equations and the stability of the equilibrium of some kinetic models.