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

共 21 条

[1]

Bahouri H., 2011, GRUNDLEHREN MATH WIS, P343

[2] Sharp well-posedness results for the BBM equation [J].

Bona, Jerry L. ;

Tzvetkov, Nikolay .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 23 (04) :1241-1252

[3]

Christ M, 2003, AM J MATH, V125, P1235

[4] A note on well-posedness for Camassa-Holm equation [J].

Danchin, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 192 (02) :429-444

[5]

Danchin R., 2001, DIFFERENTIAL INTEGRA, V14, P953

[6] GROUPS OF DIFFEOMORPHISMS AND MOTION OF AN INCOMPRESSIBLE FLUID [J].

EBIN, DG ;

MARSDEN, J .

ANNALS OF MATHEMATICS, 1970, 92 (01) :102-&

[7] Holder continuity of the solution map for the Novikov equation [J].

Himonas, A. Alexandrou ;

Holmes, John .

JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (06)

[8] ON WELL-POSEDNESS OF THE DEGASPERIS-PROCESI EQUATION [J].

Himonas, A. Alexandrou ;

Holliman, Curtis .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 (02) :469-488

[9] Non-Uniform Dependence for the Periodic CH Equation [J].

Himonas, A. Alexandrou ;

Kenig, Carlos ;

Misiolek, Gerard .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (06) :1145-1162

[10]

Himonas AA, 2009, DIFFER INTEGRAL EQU, V22, P201

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