Abstract

In this paper, we provide a new approach to get global well-posedness for the 3D liquid crystal system with large vertical velocity in the critical L2 framework. The novelty is that there is not one additional derivative when we treat the pressure. Furthermore, our idea can be applied to get global well-posedness for the 3D damped Euler equations with large vertical velocity, while the previous ideas in Wan (Dyn. Syst. 37, 5521–5539, 2017) seem not effective.

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