Ill-posedness for the Burgers equation in Sobolev spaces

被引：2
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：
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2024年 / 55卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Burgers equation; Ill-posedness; DISPERSIVE PERTURBATIONS; WELL-POSEDNESS; CAMASSA-HOLM;
D O I：
10.1007/s13226-022-00357-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the Cauchy problem for the Burgers equation in the line. We shall prove that this problem is ill-posed in the Sobolev space H-s (R) with 1 <= s <= 3/2 in the sense of "norm inflation" by constructing an explicit example of initial data.
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页码：189 / 197
页数：9
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