In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion… (More)

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R. We first prove the local existence of unique strong solutions… (More)

We consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. In this paper, we establish the existence of a weak solution (ρ, u, n) of such a system when… (More)

Abstract. The purpose of this note is to analyze a two-fluid model which can be understood as a generalization of Keller–Segel type of models for cell migration due to random motion and chemotaxis. A… (More)

We consider a compressible gas-liquid drift-flux model with a general slip law commonly used to describe realistic two-phase flow scenarios. The slip law will introduce a difference in the magnitude… (More)

We consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. As mentioned in [12], the weak solution was obtained with the initial density having a… (More)

In this paper, we prove the existence of global weak solutions to the compressible NavierStokes equations when the pressure law is in two variables. The method is based on the Lions argument and the… (More)