scholarly journals The Cauchy problem for a two-component Novikov equation in the critical Besov space

2015 ◽  
Vol 423 (1) ◽  
pp. 120-135 ◽  
Author(s):  
Hao Tang ◽  
Zhengrong Liu
Keyword(s):  
Cauchy Problem ◽  
Besov Space ◽  
Critical Besov Space ◽  
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 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
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