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On the long term dynamics of the Landau-DeGennes gradient flow with Professor Atanas Stefanov

This is a past event.

Thursday, November 17, 2022 at 3:45pm to 4:45pm

DM - Deuxieme Maison, 409A
11200 SW 8th ST, Deuxieme Maison, Miami, Florida 33199

This week's colloquium speaker is Professor Atanas Stefanov from the University of Alabama-Birmingham. The talk is scheduled for Thursday, Nov 17, from 3:45-4:45pm, in room DM 409A.

Prof. Stefanov will be hosted by Svetlana.

Abstract: The dynamic behavior of nematic liquid crystals is an ubiquitous and well-studied problem. The main object is a second order moment of the probability density function of a nematic liquid crystal embedded in $R^d$ . This is a symmetric zero-trace matrix, which describes the orientation of liquid crystal molecules. The relevant model for these matrices is the gradient flow of the Landau-deGennes energy functional, in the physically important spatial dimensions $d=2,3$.  We establish global well-posedness and global exponential time decay bounds for large $H^1$data in the 2D case, and uniform bounds for large data in 3D. This is the best possible outcome in 3D, given that steady states do exist (hence they do not decay), at least for some coefficient configurations.

In addition, we establish leading order terms and sharp asymptotics for the said dynamics in 2D. In 3D, we similarly isolate the leading order term, under the necessary assumption that a given (and possibly initially large) solution converges to zero. Finally, we derive the sharp asymptotics for the correlation functional, which was derived earlier by Kirr-Wilkinson-Zarnescu (J. Stat. Phys. 2014) in 3D, through a different method and for small data only.

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Meeting ID: 984 3919 7040

Passcode: FIU2022

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Department of Mathematics and Statistics


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