This dissertation focuses on the relative energy analysis of twospecies fluids composed of charged particles. It presents a formal derivation of the relative energy identity for both the bipolar EulerMaxwell system and the unmagnetized case of the bipolar EulerPoisson system. Furthermore, the dissertation explores several applications of the relative energy method to EulerPoisson systems, enabling a comprehensive stability analysis of these systems. The first application establishes the highfriction limit of a bipolar EulerPoisson system with friction, converging towards a bipolar driftdiffusion system. Moreover, the second application investigates the limits of zeroelectronmass and quasineutrality in a bipolar EulerPoisson system. In the former limit, a nonlinear adiabatic electron system is obtained, while the combined limit yields an Euler system. A weakstrong uniqueness principle for a singlespecies EulerPoisson system in the whole space is also established. This principle is further extended to an EulerRiesz system, considering a more general interaction potential. The theory of Riesz potentials, along with representation formulas for the potentials, is employed to overcome the technical challenges in these studies.
Date of Award  Sep 12 2023 

Original language  English (US) 

Awarding Institution   Computer, Electrical and Mathematical Sciences and Engineering


Supervisor  Athanasios Tzavaras (Supervisor) 
