Preprint 2005-006

Global solutions of the Hunter–Saxton equation

Alberto Bressan and Adrian Constantin

Abstract: We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equation modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.

Paper:: Available as PDF (240 Kbytes), Postscript (1.6 Mbytes) or gzipped PostScript (392 Kbytes; uncompress using gunzip).
Author(s):: Alberto Bressan; Adrian Constantin, <adrian@maths.tcd.ie>
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Submitted by:: <adrian@maths.tcd.ie> January 25 2005.

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