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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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