On the Cauchy problem of a new integrable two-component Novikov equation

2020 ◽  
Vol 193 (2) ◽  
pp. 361-381
Author(s):  
Yongsheng Mi ◽  
Daiwen Huang
Keyword(s):  
Cauchy Problem ◽  
Two Component ◽  
The Cauchy Problem ◽  
Novikov Equation

scholarly journals On the Cauchy Problem for the Two-Component Novikov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Transport Equation ◽  
Besov Spaces ◽  
Well Posedness ◽  
Two Component ◽  
The Cauchy Problem ◽  
Novikov Equation

We are concerned with the Cauchy problem of two-component Novikov equation, which was proposed by Geng and Xue (2009). We establish the local well-posedness in a range of the Besov spaces by using Littlewood-Paley decomposition and transport equation theory which is motivated by that in Danchin's cerebrated paper (2001). Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time, which extend some results of Himonas (2003) to more general equations.

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.

scholarly journals The Cauchy problem for a generalized Novikov equation

2017 ◽  
Vol 37 (6) ◽  
pp. 3503-3519 ◽  
Author(s):  
Rudong Zheng ◽  
◽  
Zhaoyang Yin ◽  
Keyword(s):  
Cauchy Problem ◽  
The Cauchy Problem ◽  
Novikov Equation ◽  
A Generalized Novikov Equation
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