Research

1. The Relativistic Vlasov-Maxwell Equations in Two Space Dimensions. Research Advisor: Neel Patel. Funding: F040585-Sub of F040563-CAREER.
   This paper is a result of my research project in the 2020 University of Michigan Mathematics REU.

   Abstract: The global existence and smoothness of the 3-dimensional relativistic Vlasov-Maxwell system, a longstanding problem in analysis, has not yet been proved without invoking further assumptions. Glassey-Schaeffer [2], [4] proved that in two spatial dimensions, there exist unique global in time classical solutions, given regular initial data with compact support in the momentum variable. Luk-Strain [5] proved a more general case, instead requiring that the initial data in the momentum variable has polynomial decay. In this paper, we consider the case where there are two spatial dimensions and the initial data is symmetric under rotations. Our results work towards a bound of the support of particle velocities for large time and large radius.