Analysis Seminar

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Well-Posedness of the Nematic Liquid Crystal Flow in \(L3_{uloc}(R3)\)

Speaker: Wang Changyou, University of Kentucky

Location: Warren Weaver Hall 1302

Date: Thursday, October 25, 2012, 11 a.m.

Synopsis:

In this talk, I will consider a simplified Ericksen-Leslie system modeling the incompressible nematic liquid crystal flow. For any initial data \((u_0,d_0)\), with \((u_0,\nabla d_0)\) belonging to \(L3_{uloc}(R3)\) -- the space of uniformly locally \(L3\)-integrable functions, we will show the local well-posedness provided that the \(L3_{uloc}(R3)\)-norm of \((u_0,\nabla d_0)\) is small. A characterization of the first singular time for such a solution will also be given. This is a joint work with Jay Hineman.