The electrostatic screening properties of ionic fluids are of paramount importance in
countless physical processes. Yet the screening behavior of ionic conductors out of thermal …

In this work, we will introduce a general framework to derive the thermodynamics of a fluid
mechanical system, which guarantees the consistence between the energetic variational …

We establish three partial differential equation models describing the thermodynamic
behavior of a fluid by combining the energetic variational approach, appropriate constitutive …

We study the Cauchy problem of the new model of the three dimensional inertial nematic
electrolyte, which models the N-species charged particles diffuse and advect in the nematic …

We study the continuity of weak solutions for quasilinear elliptic systems with source terms of
critical growth arising from a transport-energy structure. The latter occurs frequently in …

In this paper, we study the well-posedness of the Poisson--Nernst--Planck system with no-
flux boundary condition and singular permanent charges in two dimensions. The main …

Thermodynamics has been the foundation of many models of biological and technological
systems. But thermodynamics is static and is misnamed. A more suitable name is …

We investigate the global existence of strong solutions to a non-isothermal ideal gas model
derived from an energy variational approach. We first show the global well-posedness in the …

Recently, energetic variational approach was employed to derive models for non-isothermal
electrokinetics by Liu et. al\cite {Liu-Wu-Liu-CMS2018}. In particular, the Poisson-Nernst …

In this work, the Poisson-Nernst-Planck-Fourier system in three dimensions is considered.
For when the initial data regards a small perturbation around the constant equilibrium state …