arXiv subjects

Yuanxiang Yan

Publications and source records attributed to Yuanxiang Yan.

4 recordsLinked to original sources

arXiv2026

Global strong solutions for 1D compressible Navier-Stokes/Cahn-Hilliard equations with vacuum

In this paper, we study the initial-boundary value problem of the 1D compressible Navier--Stokes/Cahn--Hilliard system with vacuum. We establish the global existence and uniqueness of strong solutions to this initial-boundary value problem. No any initial compatibility conditions are required via time weighted techniques, which leads to a loss of regularity near the initial time. Therefore, the uniqueness of solutions obtained in this paper is even more challenging. To address this issue, we establish refined growth estimates and singular-in-time weighted energy estimates that induce a Gronwall-type structure, which ultimately allows us to close the uniqueness proof in Eulerian coordinates without passing to Lagrangian coordinates.

math.AP↗

arXiv2025

Navier-Stokes/Allen-Cahn system with moving contact line

In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid wall) moves along the wall when one fluid replaces the other, such as in liquid spreading or oil-water displacement. The system is equipped with the generalized Navier boundary conditions (GNBC) for the fluid velocity ${\boldsymbol u}$, and dynamic boundary condition or relaxation boundary condition for the phase field variable $ϕ$. We first obtain the local-in-time existence of unique strong solutions to the 2D and 3D Navier-Stokes/Allen-Cahn (NSAC) system with generalized Navier boundary conditions and dynamic boundary condition. For the 2D case in channels, we further show these solutions can be extended to any large time $T$. Additionally, we prove the local-in-time strong solutions for systems with generalized Navier boundary conditions and relaxation boundary condition in 3D channels. Finally, we establish a global unique strong solution accompany with some exponential decay estimates when the fluids are near phase separation states and the contact angle closes to 90 degrees or the fluid-fluid interface tension constant is small.

math.AP↗

arXiv2024

Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel

In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is the phase field model for the moving contact line problem in fluid mechanics. We establish the existence and uniqueness of local-in-time strong solution to this initial boundary value problem in 2D. To our knowledge, this is the first result to give the local-in-time well-posedness of Navier-Stokes/Cahn-Hilliard system with generalized Navier boundary condition and relaxation boundary condition. This result provides a rigorous mathematical analysis to confirm that the physical and numerical results by Qian-Wang-Sheng [Phys. Rev. E 68 (2003), 016306, 1-15; J. Fluid Mech. 564 (2006), 333-360] are well-posed and reasonable.

math.AP↗

arXiv2021

Strong Solutions for 1D Compressible Navier-Stokes/Allen-Cahn System with Phase Variable Dependent Viscosity

This paper is concerned with a non-isentropic compressible Navier-Stokes/Allen-Cahn system with phase variable dependent viscosity $η(χ)=χ^α$ and temperature dependent heat-conductivity $κ(θ)=θ^β$. We show the global existence of strong solutions under some assumptions on growth exponent $α$ and initial data. It is worth noting that the initial data could be large if $α\ge0$ is small, and the growth exponent $β>0$ can be arbitrary large.

math.AP↗