On the Continuity of the Solution Map of the Euler-Poincare Equations in Besov Spaces

被引：0

作者：

Li, Min ^{[1
]}

Liu, Huan ^{[2
]}

机构：

[1] Jiangxi Univ Finance & Econ, Dept Math, Nanchang 330032, Peoples R China

[2] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang 330032, Peoples R China

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2023年 / 25卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Euler-Poincare equations; Nowhere uniformly continuous; Besov spaces; Data-to-solution map; SHALLOW-WATER EQUATION; CAMASSA-HOLM; NONUNIFORM DEPENDENCE; WELL-POSEDNESS; ILL-POSEDNESS; INITIAL DATA; EXISTENCE; BREAKING; FAMILY;

D O I：

10.1007/s00021-023-00778-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By constructing a series of perturbation functions through localization in the Fourier domain and using a symmetric form of the system, we show that the data-to-solution map for the Euler-Poincare'equations is nowhere uniformly continuous in B-p,r(s)(R-d) with s > max{1+ d/2, 3/2 } and (p, r) ? (1, 8) x [1, 8). This improves our previous result (Li et al. in Nonlinear Anal RWA 63:103420, 2022) which shows the data-to-solution map for the Euler-Poincare' equations is non-uniformly continuous on a bounded subset of B-p,r(s)(R-d) near the origin.

引用

页数：12

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