Blow up criterion for nematic liquid crystal flows

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

Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy

In this paper we prove the existence of global in time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible Navier-Stokes system for the macroscopic velocity u is coupled to a nonlinear convective parabolic equation describing the evolution of the Q-tensor Q, namely...

A blow-up criterion in terms of the density for compressible viscous flows

We study an initial boundary value problem for the two-dimensional Navier-Stokes equations of compressible fluids in the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum (ρ = 0) and the concentration of mass (ρ = ∞), then a local strong solution can be continued globally in time.