arXiv subjects

Bohan Ouyang

Publications and source records attributed to Bohan Ouyang.

3 recordsLinked to original sources

arXiv2026

The Cahn--Hilliard--Darcy--Forchheimer system with surfactant: Existence and long-time behavior of global weak solutions

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity $\boldsymbol{u}$ coupled with two Cahn--Hilliard equations involving Flory--Huggins type singular potentials, one for the phase-field variable $\phi$, the difference in volume fractions of the two fluids, and the other for the surfactant concentration $\psi$. We study the initial boundary value problem in two or three dimensions, with impermeability boundary conditions for $\boldsymbol{u}$ and homogeneous Neumann boundary conditions for $(\phi, \psi)$ and their associated chemical potentials. First, we establish the existence of global weak solutions via an implicit-explicit time-discretization scheme based on the energy dissipation law. Furthermore, applying the seminal results of the first and third authors (arXiv:2510.17296), we prove that every weak solution satisfying an energy inequality converges to a single equilibrium as time tends to infinity. In sharp contrast with the available literature on similar models, in this case weak solutions are enough to guarantee the uniqueness of asymptotic limits, without the necessity of any further eventual regularization.

math.AP↗

arXiv2025

Global Weak Solutions of a Thermodynamically Consistent Diffuse Interface Model for Nonhomogeneous Incompressible Two-phase Flows with a Soluble Surfactant

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or three dimensions. The resulting hydrodynamic system consists of a nonhomogeneous Navier-Stokes system for the (volume averaged) velocity $\mathbf{u}$ and a coupled Cahn-Hilliard system for the phase-field variables $\phi$ and $\psi$ that represent the difference in volume fractions of the binary fluids and the surfactant concentration, respectively. For the initial boundary value problem with physically relevant singular potentials subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the chemical potentials, we first establish the existence of global weak solutions in the case of non-degenerate mobilities based on a suitable semi-implicit time discretization. Next, we prove the existence of global weak solutions for a class of general degenerate mobilities, with the aid of a new type of approximations for both the mobilities and the singular parts of the potential densities.

math.AP↗

arXiv2024

Regularity and long-time behavior of global weak solutions to a coupled Cahn-Hilliard system: the off-critical case

We consider a diffuse interface model that describes the macro- and micro-phase separation processes of a polymer mixture. The resulting system consists of a Cahn-Hilliard equation and a Cahn-Hilliard-Oono type equation endowed with the singular Flory-Huggins potential. For the initial boundary value problem in a bounded smooth domain of $\mathbb{R}^d$ ($d\in\{2,3\}$) with homogeneous Neumann boundary conditions for the phase functions as well as chemical potentials, we study the regularity and long-time behavior of global weak solutions in the off-critical case, i.e., the mass is not conserved during the micro-phase separation of diblock copolymers. By investigating an auxiliary system with viscous regularizations, we show that every global weak solution regularizes instantaneously for $t>0$. In two dimensions, we obtain the instantaneous strict separation property under a mild growth condition on the first derivative of potential functions near pure phases $\pm 1$, while in three dimensions, we establish the eventual strict separation property for sufficiently large time. Finally, we prove that every global weak solution converges to a single equilibrium as $t\to +\infty$.

math.AP↗