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Global existence of solutions to the 2D incompressible liquid crystal flow with fractional diffusion. (English) Zbl 1311.35220

Summary: In this paper, we consider the global regularity for 2D liquid crystal model with fractional diffusion. Global regularity is proved for two cases: \(0<\beta<1\), \(\alpha+\beta=2\) or \(\beta=1\), \(\alpha>0\).

MSC:

35Q35 PDEs in connection with fluid mechanics
76A15 Liquid crystals
26A33 Fractional derivatives and integrals
35B65 Smoothness and regularity of solutions to PDEs
60J60 Diffusion processes
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