117 citations · 146 across the 12 of their papers we have counts for
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Finite-Time Vanishing of Vacuum and Large-Time Behavior of the Multi-Dimensional Degenerate Compressible Navier-Stokes Equations with Large Spherically Symmetric Initial Data
Qinghao Lei, Zhilei Liang
In this paper, we study the two- and three-dimensional barotropic compressible Navier-Stokes equations with degenerate density-dependent viscosity coefficients in the whole space o…
On weak solutions for the stationary Cahn-Hillard-Navier-Stokes equations with singular potential
Zhilei Liang, Sen Liu, Jiangyu Shuai +1
The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy de…
Weak solutions to the equations of stationary compressible flows in active liquid crystals
Zhilei Liang, Apala Majumdar, Dehua Wang +1
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes e…
Long-time behavior of weak solutions for compressible Navier-Stokes equations with degenerate viscosity
Zhilei Liang
The long-time regularity and asymptotic of weak solutions are studied for compressible Navier-Stokes equations with degenerate viscosity in a bounded periodic domain in two and thr…
Weak solutions to the stationary Cahn-Hillard/Navier-Stokes equations for compressible fluids
Zhilei Liang, Dehua Wang
We are concerned with the Cahn-Hilliard/Navier-Stokes equations for the stationary compressible flows in a three-dimensional bounded domain. The governing equations consist of the…
Stationary Cahn-Hilliard-Navier-Stokes equations for the diffuse interface model of compressible flows
Zhilei Liang, Dehua Wang
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a…
A Kato-type criterion for vanishing viscosity near the Onsager's critical regularity
Robin Ming Chen, Zhilei Liang, Dehua Wang
We consider a vanishing viscosity sequence of weak solutions of the three-dimensional Navier--Stokes equations on a bounded domain. In a seminal paper [25] Kato showed that for suf…
Energy equality in compressible fluids with physical boundaries
Robin Ming Chen, Zhilei Liang, Dehua Wang +1
We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an - regularity conditions…
Vanishing pressure limit for compressible Navier-Stokes equations with degenerate viscosities
Zhilei Liang
In this paper we study a vanishing pressure process for highly compressible Navier-Stokes equations as the Mach number tends to infinity. We first prove the global existence of wea…
Local strong solution for the viscous compressible and heat-conductive fluids with vacuum in 2D space
Zhilei Liang
This paper considers the Cauchy problem of equations for the viscous compressible and heat-conductive fluids in the two-dimensional(2D) space. We establish the local existence theo…
Large-time behavior for spherically symmetric flow of viscous polytropic gas in exterior unbounded domain with large initial data
Zhilei Liang
This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in with . We sh…
Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data
Jing Li, Zhilei Liang
This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes syst…
On Classical Solutions to the Cauchy Problem of the Two-Dimensional Barotropic Compressible Navier-Stokes Equations with Vacuum
Jing Li, Zhilei Liang
This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, th…