On the regularity of weak small solution of a gradient flow of the Landau–de Gennes energy

Huang, Tao; Zhao, Na

doi:10.1090/proc/14337

On the regularity of weak small solution of a gradient flow of the Landau–de Gennes energy
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by Tao Huang and Na Zhao

Proc. Amer. Math. Soc. 147 (2019), 1687-1698

DOI: https://doi.org/10.1090/proc/14337

Published electronically: January 8, 2019

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Abstract:

For a gradient flow of the Landau–de Gennes energy, the unique global weak solution of initial and boundary value problem in dimension two has been constructed by Iyer–Xu–Zarnescu [Math. Models Methods Appl. Sci. 25 (2015), no. 8, 1477–1517] with small initial data. We investigate the regularity of such a solution, and prove that the weak small solution constructed in that paper is actually regular.

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