Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows

Well-posedness of Nematic Liquid Crystal Flow

In this paper, we establish the local well-posedness for the Cauchy problem of the simplified version of hydrodynamic flow of nematic liquid crystals (1.1) in R3 for any initial data (u0, d0) having small L3 uloc -norm of (u0,∇d0). Here L3uloc(R 3) is the space of uniformly locally L3-integrable functions. For any initial data (u0, d0) with small ‖(u0,∇d0)‖L3(R3), we show that there exists a un...

Blow up criterion for compressible nematic liquid crystal flows in dimension three

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 for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of grad...

Strong solutions of the compressible nematic liquid crystal flow

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 provided that the initial data ρ0, u0, d0 are sufficiently regular and satisfy a natural compatibility condition. The initial density function ρ0 may vanish on an open subset (i.e., an initial vacuu...

A Regularity Criterion for the Nematic Liquid Crystal Flows

Global Well-posedness of Compressible Bipolar Navier–Stokes–Poisson Equations

We consider the initial value problem for multi-dimensional bipolar compressible Navier– Stokes–Poisson equations, and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.