Abstract
We prove the local well-posedness of the Ericksen–Leslie system, and the global well-posedness for small initial data under a physical constraint condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg–Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.
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Communicated by F. Lin
P. Zhang is partly supported by NSF of China under Grant 50930003 and 21274005.
Z. Zhang is partially supported by NSF of China under Grant 10990013 and 11071007, Program for New Century Excellent Talents in University and Fok Ying Tung Education Foundation.
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Wang, W., Zhang, P. & Zhang, Z. Well-Posedness of the Ericksen–Leslie System. Arch Rational Mech Anal 210, 837–855 (2013). https://doi.org/10.1007/s00205-013-0659-z
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DOI: https://doi.org/10.1007/s00205-013-0659-z