On the Non-Isothermal Electrodiffusion and Nernst-Planck-Boussinesq System

Explore the mathematical analysis of the Nernst-Planck-Boussinesq (NPB) system in this 44-minute conference talk that examines a coupled model combining Nernst-Planck equations with the Boussinesq approximation to describe ionic electrodiffusion in incompressible fluids under non-isothermal conditions. Discover the unique nonlinear structure of the electromigration term influenced by temperature reciprocals, which distinguishes the NPB system from other electrodiffusion models like the Nernst-Planck-Navier-Stokes system and creates distinct mathematical challenges. Learn about the analytical properties of the system, including global existence of weak solutions in three dimensions and long-time behavior analysis focusing on exponential convergence to steady states. Gain insights into advanced mathematical modeling techniques for electrochemical systems that account for temperature variations and their impact on ionic transport phenomena. Understand the theoretical foundations and mathematical rigor required to analyze complex coupled partial differential equation systems in electrochemical modeling applications.