On the Cauchy Problem for the Two-Component 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'...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/810725 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562883741876224 |
|---|---|
| author | Yongsheng Mi Chunlai Mu Weian Tao |
| author_facet | Yongsheng Mi Chunlai Mu Weian Tao |
| author_sort | Yongsheng Mi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7d66e5bde9e64eeab8c5f528fecd7b65 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7d66e5bde9e64eeab8c5f528fecd7b652025-02-03T01:21:28ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/810725810725On the Cauchy Problem for the Two-Component Novikov EquationYongsheng Mi0Chunlai Mu1Weian Tao2College of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaCollege of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, ChinaWe 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.http://dx.doi.org/10.1155/2013/810725 |
| spellingShingle | Yongsheng Mi Chunlai Mu Weian Tao On the Cauchy Problem for the Two-Component Novikov Equation Advances in Mathematical Physics |
| title | On the Cauchy Problem for the Two-Component Novikov Equation |
| title_full | On the Cauchy Problem for the Two-Component Novikov Equation |
| title_fullStr | On the Cauchy Problem for the Two-Component Novikov Equation |
| title_full_unstemmed | On the Cauchy Problem for the Two-Component Novikov Equation |
| title_short | On the Cauchy Problem for the Two-Component Novikov Equation |
| title_sort | on the cauchy problem for the two component novikov equation |
| url | http://dx.doi.org/10.1155/2013/810725 |
| work_keys_str_mv | AT yongshengmi onthecauchyproblemforthetwocomponentnovikovequation AT chunlaimu onthecauchyproblemforthetwocomponentnovikovequation AT weiantao onthecauchyproblemforthetwocomponentnovikovequation |