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

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.

preprint2011arXivOpen access
Marcus Wunsch
math.AP
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Marcus Wunsch

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