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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…
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…