Uniqueness of conservative solutions for the Hunter-Saxton equation

被引：5
作者：
Grunert, Katrin [1 ]
Holden, Helge [1 ]
机构：
[1] NTNU Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway
来源：
RESEARCH IN THE MATHEMATICAL SCIENCES | 2022年 / 9卷 / 02期
关键词：
Hunter-Saxton equation; Uniqueness; Conservative solutions; HYPERBOLIC VARIATIONAL EQUATION; CAMASSA-HOLM EQUATION; ASYMPTOTIC EQUATION; GLOBAL-SOLUTIONS; GEODESIC-FLOW; EXISTENCE;
D O I：
10.1007/s40687-022-00314-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the Hunter-Saxton equation u(t) + uu(x) = 1/4 ( integral(x)(-infinity) d mu(t, z) integral(infinity)(x) d mu(t, z)) and mu(t) + (u mu)(x) = 0 has a unique, global, weak, and conservative solution (u, mu) of the Cauchy problem on the line.
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页数：54
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