oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Weak geodesic flow on a semi-direct product and global solutions to the periodic Hunter-Saxton system  [PDF]
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.
On the Cauchy problem of a periodic 2-component $μ$-Hunter-Saxton equation  [PDF]
Jingjing Liu,Zhaoyang Yin
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.
Blow-up phenomena and global existence for a periodic two-component Hunter-Saxton system  [PDF]
Jingjing Liu,Zhaoyang Yin
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.
The Cauchy problem of a periodic 2-component μ-Hunter-Saxton system in Besov spaces  [PDF]
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.
Global existence for the generalized two-component Hunter-Saxton system  [PDF]
Hao Wu,Marcus Wunsch
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].
The Hunter-Saxton system and the geodesics on a pseudosphere  [PDF]
Jonatan Lenells,Marcus Wunsch
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.
The periodic Cauchy problem of the modified Hunter-Saxton equation  [PDF]
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.
A 2-component $μ$-Hunter-Saxton equation  [PDF]
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.
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems  [PDF]
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].
A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton system  [PDF]
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.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.