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 Marcus Wunsch Mathematics , 2011, 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.
 Mathematics , 2010, Abstract: In this paper, we study the Cauchy problem of a periodic 2-component $\mu$-Hunter-Saxton system. We first establish the local well-posedness for the periodic 2-component $\mu$-Hunter-Saxton system by Kato's semigroup theory. Then, we derive precise blow-up scenarios for strong solutions to the system. Moreover, we present a blow-up result for strong solutions to the system. Finally, we give a global existence result to the system.
 Mathematics , 2010, Abstract: This paper is concerned with blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system. We first derive the precise blow-up scenario for strong solutions to the system. Then, we present several new blow-up results of strong solutions and a new global existence result to the system. Our obtained results for the system are sharp and improve considerably earlier results.
 Jingjing Liu Mathematics , 2012, Abstract: This paper is concerned with the local well-posedness and the precise blow-up scenario for a periodic 2-component \mu-Hunter-Saxton system in Besov spaces. Moreover, we state a new global existence result to the system. Our obtained results for the system improve considerably earlier results.
 Mathematics , 2010, DOI: 10.1007/s00021-011-0075-9 Abstract: We study the global existence of solutions to a two-component generalized Hunter-Saxton system in the periodic setting. We first prove a persistence result of the solutions. Then for some particular choices of parameters $(\alpha, \kappa)$, we show the precise blow-up scenarios and the existence of global solutions to the generalized Hunter-Saxton system under proper assumptions on the initial data. This significantly improves recent results obtained in [M. Wunsch, DCDS Ser. B 12 (2009), 647-656] and [M. Wunsch, SIAM J. Math. Anal. 42 (2010), 1286-1304].
 Mathematics , 2012, Abstract: We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explicit solution formulae for the Hunter-Saxton system. Using this geometric intuition, we conclude by constructing global weak solutions. The main novelty compared with similar previous studies is that the metric is indefinite.
 Feride Tiglay Mathematics , 2005, Abstract: We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for continuously differentiable initial data. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem.
 Dafeng Zuo Physics , 2010, DOI: 10.1088/0266-5611/26/8/085003 Abstract: In this paper, we propose a two-component generalization of the generalized Hunter-Saxton equation obtained in \cite{BLG2008}. We will show that this equation is a bihamiltonian Euler equation, and also can be viewed as a bi-variational equation.
 Martin Kohlmann Mathematics , 2010, DOI: 10.1088/1751-8113/44/22/225203 Abstract: In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group $\Diff(\S)$ with a space of scalar functions on $\S$ we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2$\mu$HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].
 Anders Nordli Mathematics , 2015, Abstract: We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.
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