Nonlinear Partial Differential Equations

Date: April 30, 2024

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Quyuan Lin, Clemson University

Title: On the three-dimensional Nernst-Planck-Boussinesq system

Abstract: Electrodiffusion of ions is a phenomenon that takes place in electrolyte solutions when charged ions are transported in a fluid under the influence of an electric field. It has various real-world applications in neuroscience, semiconductor theory, water purification, desalination, ion separation, etc. In this talk, I will introduce the Nernst-Planck-Boussinesq (NPB) system, a new ionic electrodiffusion model that incorporates variational temperature and is forced by buoyancy force stemming from temperature and salinity fluctuations. The electromigration term in the NPB system displays a complex nonlinear structure influenced by the reciprocal of the temperature, which distinguishes its mathematical aspects from other electrodiffusion models studied in the literature, such as the Nernst-Planck-Navier-Stokes and the Nernst-Planck-Euler systems. I will discuss the global existence of weak solutions to the 3D NPB system as well as the long-time dynamics of these weak solutions and their exponential decay in time to steady states.