Global well-posedness for the viscous shallow water system with Korteweg type |
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| Authors: | Jinlu Li Zhaoyang Yin |
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| Institution: | 1. School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, China.;2. Department of Mathematics, Sun Yat-sen University, Guangzhou, China.lijl29@mail2.sysu.edu.cn;4. Department of Mathematics, Sun Yat-sen University, Guangzhou, China.;5. Faculty of Information Technology, Macau University of Science and Technology, Macau, China. |
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| Abstract: | In this paper, we study the Cauchy problem for a viscous shallow water system with Korteweg type in Sobolev spaces. We first establish the local well-posedness of the solution by using the Friedrich method and compactness arguments. Then, we prove the global existence of the solution to the system for the small initial data. |
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| Keywords: | Viscous shallow water system Korteweg type global well-posedness |
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