Caltech/UCLA/USC Joint Analysis Seminar

Series: Caltech/UCLA/USC Joint Analysis Seminar Series

Nematic Liquid crystal flows with free boundary

Yannick Sire, Department of Mathematics, Johns Hopkins University,

UCLA, MS 6221

I will introduce a new parabolic system for the flow of nematic liquid crystals, enjoying a free boundary condition. After recent works related to the construction of blow-up solutions for several critical parabolic problems (such as the Fujita equation, the heat flow of harmonic maps, liquid crystals without free boundary, etc...), I will construct a physically relevant weak solution blowing-up in finite time. We make use of the so-called inner/outer parabolic gluing. Along the way, I will present a set of optimal estimates for the Stokes operator with Navier slip boundary conditions. I will state several open problems related to the partial regularity of the system under consideration. This is joint work with F.-H. Lin (NYU), Y. Zhou (JHU) and J. Wei (UBC).

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