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The global weak solutions to the Cauchy problem of the generalized Novikov equation |
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| Authors: | Yongye Zhao Yongsheng Li Wei Yan |
| Institution: | 1. Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510640, P.R. China.zhao.yongye@mail.scut.edu.cn;3. Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, 510640, P.R. China.;4. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, P.R. China. |
| Abstract: | In this paper, we study the Cauchy problem of the generalized Novikov equation. We first show that under suitable condition, the strong solution exists globally via some a priori estimates. Then, we prove the existence and uniqueness of global weak solutions by the approximation method. We also obtain the exact peaked solutions. |
| Keywords: | generalized Novikov equation Cauchy problem global strong solution global weak solutions peaked solutions |