Non-uniform dependence of the data-to-solution map for the Hunter-Saxton equation in Besov spaces

被引：9
作者：
Holmes, John [1 ]
Tiglay, Feride [2 ]
机构：
[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA
[2] Ohio State Univ, Dept Math, Newark, OH 43055 USA
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2018年 / 18卷 / 03期
关键词：
Well-posedness; Initial value problem; Cauchy problem; Besov spaces; Sobolev spaces; Multi-linear estimates; Hunter-Saxton equation; PERIODIC CAUCHY-PROBLEM; CAMASSA-HOLM EQUATION; WELL-POSEDNESS; ILL-POSEDNESS; CH EQUATION;
D O I：
10.1007/s00028-018-0436-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Cauchy problem for the Hunter-Saxton equation is known to be locally well posed in Besov spaces B-2,r(s) on the circle. We prove that the data-to-solution map is not uniformly continuous from any bounded subset of B(2,)(r)s to C([0, T]; B(2,)(r)s). We also show that the solution map is Holder continuous with respect to a weaker topology.
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页码：1173 / 1187
页数：15
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