Ill-posedness for the Euler equations in Besov spaces

被引：1

作者：

Li, Jinlu ^{[1
]}

Yu, Yanghai ^{[2
]}

Zhu, Weipeng ^{[3
]}

机构：

[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[3] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2023年 / 74卷

基金：

中国国家自然科学基金;

关键词：

Euler equations; Ill-posedness; Besov spaces; NONUNIFORM DEPENDENCE;

D O I：

10.1016/j.nonrwa.2023.103941

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, we consider the Cauchy problem to the Euler equations in Rd with d & GE; 2. We construct an initial data u0 & ISIN; B & sigma;p,& INFIN; showing that the corresponding solution map of the Euler equations starting from u0 is discontinuous at t = 0 in the metric of B & sigma;p,& INFIN; , which implies the ill-posedness for this equation in B & sigma;p,& INFIN;. We generalize the periodic result of Cheskidov and Shvydkoy (2010).& COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：9

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