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Strong solutions of the compressible nematic liquid crystal flow. (English) Zbl 1233.35168
Summary: 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 a unique strong solution 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 $$||\rho||_{L^\infty_t L^\infty_x}$$ and $$||\nabla d||_{L^3_t L^\infty_x}$$.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76A15 Liquid crystals 35D35 Strong solutions to PDEs 35B44 Blow-up in context of PDEs
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