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 $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the initial data $\rho_0, u_0, d_0$are sufficiently regular and satisfy a natural compatibility condition. The initial density function $\rho_0$ may vanish on an open subset (i.e., an initial vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities $\|\rho\|_{L^\infty_tL^\infty_x}$ and $\|\nabla d\|_{L^3_tL^\infty_x}$

Strong solutions of the compressible nematic liquid crystal flow

AbstractWe study strong solutions of the simplified Ericksen–Leslie system modeling compressible nematic liquid crystal flows in a domain Ω⊂R3. We first prove the local existence of a unique strong solution 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 vacuum may exist). We then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities ‖ρ‖Lt∞Lx∞ and ‖∇d‖Lt3Lx∞

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 gradient of liquid crystal director field.Comment: 22 page

Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one

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