Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space

被引：3

作者：

Tu, Xi ^{[1
]}

Yin, Zhaoyang ^{[2
,3
]}

机构：

[1] Foshan Univ, Dept Math, Foshan 528000, Peoples R China

[2] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China

[3] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 04期

关键词：

A generalized Camassa-Holm equation; Local well-posedness; The critical Besov space; Blow-up; Global existence; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; CAUCHY-PROBLEM; INTEGRABLE EQUATION; SHOCK-WAVES; EXISTENCE; TRAJECTORIES; BREAKING;

D O I：

10.1007/s00605-020-01371-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation in a critical Besov space. First, by using the Littlewood-Paley decomposition, transport equations theory, logarithmic interpolation inequalities and Osgood's lemma, we establish the local well-posedness for the Cauchy problem of the equation in the critical Besov space B-2,1(2)1/. Next we derive a new blow-up criterion for strong solutions to the equation. Then we give a global existence result for strong solutions to the equation. Finally, we present two new blow-up results and the exact blow-up rate for strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.

引用

页码：801 / 829

页数：29

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