96 citations · 484 across the 29 of their papers we have counts for
10 papers · 1 filter
Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects
Baoli Hao, Fanze Kong, Kei Fong Lam +1
We derive and analyze a binary Poisson-Nernst-Planck system with steric interactions and interspecies drag through the energetic variational approach. The steric effects are incorp…
On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit
Jiangyan Liang, Ning Jiang, Chun Liu +2
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion syst…
Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space
Chun Liu, Jan-Eric Sulzbach
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a genera…
On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
Patrik Knopf, Chun Liu
In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace--Beltrami equation o…
The Brinkman-Fourier System with Ideal Gas Equilibrium
Chun Liu, Jan-Eric Sulzbach
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 ap…
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
Patrik Knopf, Kei Fong Lam, Chun Liu +1
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interacti…
Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
Chia-Yu Hsieh, Tai-Chia Lin, Chun Liu +1
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Ne…
Analysis of the energy dissipation laws in multi-component phase field models
Arkadz Kirshtein, James Brannick, Chun Liu
In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved…
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamics-consistency
Francesco De Anna, Chun Liu
We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extensio…
An Energetic Variational Approach for the Cahn--Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis
Chun Liu, Hao Wu
The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have…