New Distributional Global Solutions for the Hunter-Saxton Equation
نویسندگان
چکیده
منابع مشابه
Global Solutions of the Hunter-Saxton Equation
We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data. 1 Introduction In this paper we investigate the Cauchy problem
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The Hunter–Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo the subgroup of rigid rotations equipped with a right-invariant metric. We establish several properties of this quotient space: it has constant sectional curvature equal to 1, the Riemannian exponential...
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We propose and analyze several finite difference schemes for the Hunter–Saxton equation (HS) ut + uux = 1 2 ∫ x 0 (ux) 2 dx, x > 0, t > 0. This equation has been suggested as a simple model for nematic liquid crystals. We prove that the numerical approximations converge to the unique dissipative solution of (HS), as identified by Zhang and Zheng. A main aspect of the analysis, in addition to th...
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This paper is concerned with global existence of weak solutions for a periodic twocomponent μ-Hunter-Saxton system. We first derive global existence for strong solutions to the system with smooth approximate initial data. Then, we show that the limit of approximate solutions is a global weak solution of the two-component μ-Hunter-Saxton system. 2000 Mathematics Subject Classification: 35G25, 35L05
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/809095