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Global strong solution to the density-dependent 2-D liquid crystal flows. (English) Zbl 1328.76008

Summary: The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocity \(u_0\) and small \(\nabla d_0\). We also give a regularity criterion \(\nabla d \in L^p(0, T; L^q(\Omega))((2/q) + (2/p) = 1, 2 < q \leq \infty)\) of the problem with the Dirichlet boundary condition \(u = 0\), \(d = d_0\) on \(\partial\Omega\).

MSC:

76A15 Liquid crystals
35D35 Strong solutions to PDEs
35Q35 PDEs in connection with fluid mechanics
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References:

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