scholarly journals The Cauchy problem for the modified two-component Camassa–Holm system in critical Besov space

2015 ◽  
Vol 32 (2) ◽  
pp. 443-469 ◽  
Author(s):  
Wei Yan ◽  
Yongsheng Li
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Critical Besov Space ◽  
Two Component ◽  
The Cauchy Problem

scholarly journals The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space

2020 ◽  
Vol 269 (2) ◽  
pp. 1117-1171
Author(s):  
Hong-Mei Cao ◽  
Hao-Guang Li ◽  
Chao-Jiang Xu ◽  
Jiang Xu
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Critical Besov Space ◽  
The Cauchy Problem ◽  
Kac Equation

scholarly journals The Cauchy problem for the generalized Camassa–Holm equation in Besov space

2014 ◽  
Vol 256 (8) ◽  
pp. 2876-2901 ◽  
Author(s):  
Wei Yan ◽  
Yongsheng Li ◽  
Yimin Zhang
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Holm Equation ◽  
The Cauchy Problem

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

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