Well-posedness of Nematic Liquid Crystal Flow
نویسنده
چکیده
In this paper, we establish the local well-posedness for the Cauchy problem of the simplified version of hydrodynamic flow of nematic liquid crystals (1.1) in R3 for any initial data (u0, d0) having small L3 uloc -norm of (u0,∇d0). Here L3uloc(R 3) is the space of uniformly locally L3-integrable functions. For any initial data (u0, d0) with small ‖(u0,∇d0)‖L3(R3), we show that there exists a unique, global solution to (1.1) which is smooth for t > 0 and has monotone deceasing L3-energy for t ≥ 0.
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