Well-posedness of the Ericksen-Leslie system

Abstract

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain 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.

16 pages

References in corpus (1)

• The small Deborah number limit of the Doi-Onsager equation to the Ericksen-Leslie equation

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