Regularity of solutions to the liquid crystal flows with rough initial data. (English) Zbl 1284.35345
Summary: We are concerned with the regularity of solutions to the liquid crystal flows with rough initial data in \(\mathbb{R}^n\). We prove that the solution constructed by C. Wang in [Arch. Ration. Mech. Anal. 200, No. 1, 1–19 (2011; Zbl 1285.35085)] has higher regularity. Moreover we obtain a decay estimate in time for any space derivative.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A15 | Liquid crystals |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Citations:
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