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.

引用

页码：1173 / 1187

页数：15