Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter-Saxton system

Details Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter-Saxton system Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter-Saxton system

2011-01-28

arxiv.org/abs/1101.5483v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

We give explicit solutions to the two-component Hunter-Saxton system on the unit circle. Moreover, we show how global weak solutions can be naturally constructed using the geometric interpretation of this system as a re-expression of the geodesic flow on the semi-direct product of a suitable subgroup of the diffeomorphism group of the circle with the space of smooth functions on the circle. These spatially and temporally periodic solutions turn out to be conservative.

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