On the Three-dimensional Nernst-Planck-Boussinesq System
arxiv(2024)
摘要
In this paper, we analyze a three-dimensional Nernst-Planck-Boussinesq (NPB)
system that describes ionic electrodiffusion in an incompressible viscous
fluid. This new model incorporates variational temperature and is forced by
buoyancy force stemming from temperature and salinity fluctuations, enhancing
its generality and realism. The electromigration term in the NPB system
displays a complex nonlinear structure influenced by the reciprocal of the
temperature that distinguishes its mathematical aspects from other
electrodiffusion models studied in the literature. We address the global
existence of weak solutions to the NPB system on the three-dimensional torus
for large initial data. In addition, we study the long-time dynamics of these
weak solutions and the associated relative entropies and establish their
exponential decay in time to steady states.
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