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

2011/01/28 by Marcus Wunsch, Wunsch, Marcus
Mathematics · Physics and Astronomy · #35B44 #35D30 #53C22 #58B20 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AP #msc:35B44 #msc:35D30 #msc:53C22 #msc:58B20

paper · pdf · doi:10.48550/arxiv.1101.5483

13 pages

arxiv created 2011/01/28 · openalex publication_date 2011/01/28 · arxiv updated 2011/01/31 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

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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